waves and optics formula velocity equals the product of the frequency and the wavelength formula:...

$Page 1: Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio$

Waves and optics formula

Velocity equals the product of the frequency and the wavelength

Formula: Units Index of refraction of a medium equals the ratio of the

speed of light in a vacuum and the speed of light in the medium

Formula Units

Velocity equals the product of the frequency and the wavelength

Formula: v=f Units m=1 m s s Index of refraction of a medium equals the ratio of the

speed of light in a vacuum and the speed of light in the medium

Formula Units

Velocity equals the product of the frequency and the wavelength Formula: v=f Units m=1 m s s Index of refraction of a medium equals the ratio of the speed of light

in a vacuum and the speed of light in the medium Formula n = c v Units none=m/s m/s

Snell's law: the product of the index of refraction and the sin of the incident angle equals the product of the index of refraction of the second medium and the sin of the refracted angle

n1 sin 1 = n2 sin 2

The sin of the critical angle ( Above this incident angle, will reflect, but will not refract ) equals the ratio of the index of refraction in the second medium and the index of refraction of the first medium

Sin c = n2

n1

n1 sin 1 = n2 sin 2

Sin c = n2

n1

n1 sin 1 = n2 sin 2

Sin c = n2

n1

Formula used for the relationships between image location, object location and the focal length of the lens or mirror

1 + 1 = 1 si so f

The magnification equals the ration of the image height to the object height or the negative ratio of the image location to the object location

M = hi M = - si ho so

Formula used for the relationships between image location, object location and the focal length of the lens or mirror

1 + 1 = 1 si so f

The magnification equals the ration of the image height to the object height or the negative ratio of the image location to the object location

M = hi M = - si ho so

Waves and Optics Formula

The focal length equals the radius of curvature divided by 2 for lens and mirrors

f = R 2

The focal length equals the radius of curvature divided by 2 for lens and mirrors

f = R 2

Interference formula single slit equals the d sin = m d = single slit width sin f = diffraction angle m = 1,2,.. Minima The position of xm ( 1,2 minima) equals product of the minima, wavelength , distance to screen divided by

the slit width xm = m L d

Interference formula single slit equals the d sin = m d = single slit width sin= diffraction angle m = 1,2,.. Minima The position of xm ( 1,2 minima) equals product of the minima, wavelength , distance to screen divided by

Interference formula single slit equals the d sin = m d = single slit width sin= diffraction angle m = 1,2,.. Minima The position of xm ( 1,2 minima) equals product of the minima,

wavelength , distance to screen divided by the slit width xm = m L

d

Interference formula double or multiple slit equals the d sin = m d = distance between slits sin= diffraction angle m = 1,2,.. Maxima The position of xm ( 1,2 maxima) equals product of the maxima,

d

Plane Mirror

So equals Si

Plane Mirror

So equals Si

Image is upright, virtual, and same size

Plane Mirror

So equals Si

Plane Mirror

So equals Si

Plane Mirror

So equals SiImage is upright, virtual, and same size

Plane Mirror

Image upright

Plane Mirror

Image upright, virtual,

Plane Mirror

Image upright, virtual, same size

Plane Mirror

Block ½ mirror?

Plane Mirror

Block ½ mirror? Image upright, virtual, same size

Plane Mirror

Block ½ mirror? Image upright, virtual, same sizeDimmer

Shadows

Elicpses – lunar, solar

Convex Mirror

So=10 cm

Convex Mirror

So=10 cm R=6cm f=3cm

Convex Mirror

So=10 cm R=6cm f=3cm

Concave Mirror

So=10 cm R=6cm f=+3cm

Concave Mirror

Si = 4.28 cm

Concave Mirror

Si = 4.28 cm

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Inverted Real Smaller

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

So=6cm R=6cm f=+3cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

So=6cm R=6cm f=+3cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - .429

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Inverted Real Same Size

Concave Mirror

Si = 4.29 cm

So=4.5 cm R=6cm f=+3cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 1.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Inverted Real Larger

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Inverted Real LargerParallel Rays

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Inverted Real LargerParallel Rays - No Image

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - (-15.0 cm) 2.5 cmM = - 2.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - (-15.0 cm) 2.5 cmM =+6.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - (-15.0 cm) 2.5 cmM =+6.0

Upright Virtual Larger

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - (-15.0 cm) 2.5 cmM =+6.0

Concave Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/2.5cm = 1/ si

Si = -15.0 cm

M = - si / so = - (-15.0 cm) 2.5 cmM =+6.0

Convex Mirror

Si = 4.29 cm

So=4.5 cm R=6cm f=-3cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = - 2.0

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = + .40

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = + .40

Upright Real Larger

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = + .40

Convex Mirror

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) - 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = + .40

Upright Virtual Smaller

RefractionIncident RayDistance to normal1.33 cm2.00 cm2.66 cm3.33 cm4.00 cm

Refracted Distance to Normal1.00 cm1.50 cm2.00 cm2.50 cm3.00 cm

Index of Refraction (n) n1dincident=n2drefracted

n1 = air = 1.00

n1dincident = n2

drefracted

Therefore dincident / drefracted = n2

Slope = 1.33=n2=nwater

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

Incident Distance as a function of Refracted Distance to Normal

0

24

6

0 1 2 3 4

Refracted distance

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

Incident Distance as a function of Refracted Distance to Normal

0

24

6

0 1 2 3 4

Refracted distance

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

refracted

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

refracted

n1dincident=n2drefracted

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

refracted

sinincident =dincident

radius

sinefracted = drefracted

radius

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

refracted

radius

Therefore

n1sinincident=n2sinrefracted

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident

refracted

radius

Therefore

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted

radius

Therefore

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted =7.50

radius

Therefore

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted =7.50

radius

Therefore

n1 = air = 1.0

Refraction-Snell’s LawIncident RayDistance to normal1.33 cm2.00 cm2.66 cm3.33 cm4.00 cm

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted =7.50

radius

Therefore

n1 = air = 1.0

Sin 10o = n2 = nwater = 1.33

Sin 7.5o

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted =7.50

radius

Therefore

n1 = air = 1.0

Sin 10o = n2 = nwater = 1.33

Sin 7.5o

n1 = air = 1.00

n1dincident = n2

drefracted

water

air

incident = 100

refracted =7.50

radius

Therefore

n1 = air = 1.0

Sin 10o = n2 = nwater = 1.33

Sin 7.5o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

n1 = nwater = sinefracted

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

water

air

incident = 100

refracted =13.50

n2 = air = 1.0

sinncident

sin 13.5o = n1 = nwater = 1.34

sin 10.0o

Refraction

incident

Normal

refracted r

incident

refracted r

Towards normal when

ni < nr (n=index of refraction

or optical density )

Away from normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

nair = 1.0

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

nair = 1.0

Nglass 1.3

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

nair = 1.0

Nglass1.3

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

nair = 1.0

Nglass 1.3

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

nair = 1.0

Nglass1.3

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

velocity of light decreases v = c nFrequency remainsthe same

n = vacuum

n

nglass = 1.3

nair = 1.0

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

n = vacuum

n

nair = 1.0

nglass = 1.3

Refractionincident

Normal

refracted r

incident

refracted r

Towards normal when

Away from normal

when ni > nr

n = vacuum

n

nair=1.0

nglass = 1.3

Refraction

incident

Normal

refracted r

incident

refracted r

Away from normal when

ni > nr (n=index of refraction

Toward normal

when ni > nr

velocity of light decreases v = c n

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Refraction

incident

Normal

refracted r

incident

refracted r

Toward normal

when ni > nr

Snell’s Law

Incident = 10o Refracted = 6.5o

n1 for air = 1.0 n2 = ?

100 6.50

n1sin i = n2 sin 2

n1sin i = n2 = 1.0 sin 10o =1.5sin 2 sin 6.50

Snell’s Law

n1 for air = 1.0 n2 = ?

150 9.20

n1sin i = n2 sin 2

Snell’s Law

n1 for air = 1.0 n2 = ?

200 16.10

n1sin i = n2 sin 2

Snell’s Law

Incident = 10.0o Refracted = 15.4o

n1 = ? n2 = 1.0 (air)

100

15.40

n1sin i = n2 sin 2

n1 = n2 sin 2 = = 1.0 sin 15.40 =1.5 sin 1 sin 10.00

Snell’s Law

n1 = ? n2 = 1.0 (air)

150

23.30

n1sin i = n2 sin 2

n1 = n2 sin 2 = = 1.0 sin 23.30 =1.5 sin 1 sin 15.00

Critical Angle-Total Internal Reflection

Incident = ? If n1=1.5 n2=nair=1.0

sin c = n2

n1

c = 42o

The larger the difference between n2 and n1 the smaller the ratio and the lower the critical angle

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

30.10

n1sin i = n2 sin 2

sin c = n2 =1.0

n1 1.5

c = 42o

30.10

n1sin i = n2 sin 2

Snell’s Law

n1 = ? n2 = 1.0 (air)

20.00

30.10

n1sin i = n2 sin 2

n1 = n2 sin 2 = = 1.0 sin 31.60 =1.5 sin 1 sin 20.00

sin c = n2

n1

c = 42o

Refracted = 31.6o

n1 = ? n2 = 1.0 (air)

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

Any incident angle above that critical angle will only reflect.

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

30.10

n1sin i = n2 sin 2

sin c = n2

n1

c = 42o

30.10

n1sin i = n2 sin 2

150150

Law of Reflection

10.7o

Snell’s law – Refraction

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = n2 sin f2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

36o

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.0 1.4 1.0

36o

Law of Reflection

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.4 1.0 1.41.0

How would the reflection and refraction be different ?

150150

Law of Reflection

10.7o

n1sin 1 = n2 sin 2

n1sin 1 = sin 2

n2

1.0sin 150 = sin 2

1.410.7o = 2

n1sin f1 = sin f2

n2

1.4sin 360 = sin 2

1.0 45.6o = 2

36o

45.6o

1.4 1.0 1.41.0

How would the reflection and refraction be different ?

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

So=9.0 cm R=6cm f= +3cm

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/10cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.29 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.29 cm 10 cmM = - .429

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/9cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 4.5 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 4.5 cm 9.0 cmM = - .50

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm - 1/6cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 6.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 6.0 cm 6.0 cmM = - 1.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

No Image- Parallel RaysReal Larger

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/4.5cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = 9.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - 9.0 cm 4.5 cmM = - 2.0

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Upright

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Upright Virtual

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/3cm – 1/2.1cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -7.0 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-7.0 cm 2.1 cmM = +3.33

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = .40

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = .40

Converging Lens

Si = 4.29 cm

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = .40

Converging Lens

Si = 4.29 cm

Upright Virtual Smaller

1/f = 1/so + 1/si

1/f-1/so= 1/si

1/(-3cm) – 1/4.5cm = 1/ si

Si = -1.8 cm

M = - si / so = - (-1.8 cm 4.5 cmM = .40

Compound Optical Instruement

do=___? h= ____

f1 =___ cm f2 = ___ cm

1. Measure do, f1, ,f2 h and draw rays to determine initial and final di

2. Calculate initial and final di positions3. Measure final h and determine magnification by drawing and by calculations

Compound Microscope

So=29h=.67

f=15

Si=31M=31/29M=1.07H=.75

Compound Microscope

fe=26

So=17

Compound Microscope

Compound Optical Instruement

f=26

So=17h=.75

Si=-49h = 2.0M=49/17M=2.9

Compound Microscope

Diffraction

Path length differences produce constructive Interference if

path length difference is a whole number multiples of the wavelength

Destructive Interference will occur if

path length difference is multiples of ½ of a wavelength

Diffraction

Single Slit Interference

Single Slit

max

min

Single Slit

max

min

Single Slit

max

Min

Single Slit

max

min

Single Slit Diffraction

d

Sin = opp = m hyp d m = 0,1,2… for minima

d

Sin = opp = m hyp d m = 1,2… for minima

d

Single Slit

max

min

Single Slit

max

min

L = distance to screen

Single Slit

max

min

L = distance to screen

xm

Xm distanceTo minima

Single Slit

max

min

Tan = xm

L

xm

Single Slit

max

min

Tan = xm

L

xm

Sin = m d

Single Slit

max

min

Tan = xm

L

xm

Sin = m d

Tan = sin

Single Slit

max

min

Tan = xm

L

xm

Sin = m d

Tan = sin Xm = m L d

Young’s Double Slit Experiment

Max

Sin = m = xm d L

Length (L) to screen

Max

Sin = m = xm d L

Max

Sin = m = xm d L

xm

Max

Sin = m = xm d L

xm

Max

Sin = m = xm = tan

d L

= xm d m L

xm

Multiple Slit Diffraction

Sin = m = xm d L

= xm d m L

1

0

1

m = 0 , 1,2, 3 … max

Sin = m = xm d L

= xm d m L

1

0

1

m = 0 , 1,2, 3 … max

Sin = m = xm d L

= xm d m L

1

0

1

m = 0 , 1,2, 3 … max

Sin = m = xm d L

= xm d m L

1

0

1

m = 0 , 1,2, 3 … max

Sin = m = xm = tan d L

= xm d m L m L d

1

0

1

m = 0 , 1,2, 3 … max

Sin = m = xm = tan d L

= xm d m Lxm

m L d

1

0

1

m = 0 , 1,2, 3 … max

Single, Double, Multiple SlitDiffraction

Based on constructive and destructive interference

Caused by path length differences

Caused by path length differences Geometry based on sin = m

xm=tan

d L

Caused by path length differences Geometry based on sin = m xm d L Single Slit m is for minima with broad central

maxima Double / Multiple m is for maximum

Reflection-Interference, Newton’s Rings, Thin Film Interference

Higher Index of Refraction

Lower Index of Refraction

Relected ray experience a half wavelength phase change

No phase change occurs

Air Wedge Reflection-Interference

Hair

Air

Glass

Phase change reflection

Phase change reflection – 1800 – nair< nglass

Towards normal refraction

Towards normal refraction nair < nglass

No phase change reflection nglass >nair

Away from normal refraction

Away from normal refraction – nglass> nair

Away from normal refraction

Away from normal refraction nglass > nair

speeds up

Phase change reflection

Phase change reflection nair < nglass

Towards normal refraction

Towards normal refraction nair < nglass

Towards normal

Away from normalrefraction

Away from normalRefraction nglass > nair

Towards normalNo Phase Change

Away from normal

Away fromnormal Phase Change

Toward Normal

Phase Change

Away from normal

Towards normal No Phase Change

Away from normal

Toward Normal

Away from normal

No Phase Change Phase Change

l = d + ½ + d

½ + 2d = D l

Away from normal

Toward Normal

Away from normal

No Phase Change Phase ChangeIf the path length of the light that is transmitted through the upper glass plate, then reflected off the air glass interference of the bottom plate with 180 degree phase reversal,then transmitted through the upper plate is multiples of ½ of a the path length of the light that is refracts through the upper glass plate, then reflects off the upper glass air interference without a phase change will interfer constructively.

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

½ + 2d = D l

d = distance between the plates

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

½ + 2d = D l

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

½ + 2d = D l

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

½ + 2d = D l

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Constructive Interference =n

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Constructive Interference =n

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Constructive Interference =l =m= ½ + 2dm=1/2 + 2 d

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Away from normal

Toward Normal

Away from normal

l = d + ½ + d

l = ½ + 2d

Constructive Interference =l =m= ½ + 2d 1/2 + 2 d

Thin Film Interference

Antiflective coating with an index of refractionGreater than air but less than the glass lens

nair =1.0

n thin film = 1.3 nglass = 1.7

Thin Film Interference Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction added to ½ wavelength due to phase refersal.

leffrr = nt + nt + ½ leffrr = 2nt+ ½

Reflected ray leffr = ½

Constructive inteference occurs at whole multiples of wavelength path lengthdifferences. Therefore in this case the refracted,reflected,refracted ray will showconstructive interference if 2nt = mt = mapproxiamately2nDestructive interference occurs at ½ whole multiples of wavelength path length differencesTherefore in this case the refracted,reflected,refracted ray will show destructive interferenceIf 2nt = mt=m approxiamately 2 4n

n =1.0

nthin film = 1.3

Antiflective coating with an index of refractionGreater than and the glass lens

nair =1.0

n thin film = 1.6 nglass = 1.4

Thin Film Interference Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction

leffrr = nt + nt leffrr = 2nt

Constructive inteference occurs at whole multiples of wavelength path lengthdifferences. Therefore in this case the refracted,reflected,refracted ray will showconstructive interference if 2nt = m- ½ t = m+1/2 t = (m+1/2) 2n 2nDestructive interference occurs at ½ whole multiples of wavelength path length differencesTherefore in this case the refracted,reflected,refracted ray will show destructive interferenceIf 2nt = mt = m + 2 4n 4n

n =1.0

nthin film = 1.3

Thin Film Interference Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction added to ½ wavelength due to phase refersal.

leffrr = nt + nt + ½ leffrr = 2nt+ ½

Constructive inteference occurs at whole multiples of wavelength path lengthdifferences. Therefore in this case the refracted,reflected,refracted ray will showconstructive interference if 2nt = mt = m2nDestructive interference occurs at ½ whole multiples of wavelength path length differencesTherefore in this case the refracted,reflected,refracted ray will show destructive interferenceIf 2nt = mt=m 2 4n

n =1.0

nthin film = 1.3

Thin film interference

n1 = air

n2=1.33

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

m = 2 n t m = t (thickness of film) 2n

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

n1=1.00

n2=1.33

n3=1.50

If l was 4.8 x10-7m what would the miniumum thickness need to cause Constructive interference?If l was 4.8 x10-7 m what would the miniumum thickness need to causeDestructive interference?

Summary

Constructive interference – pathlength equals m Destructive interference – pathlength equal m 2

If n1<n2>n3 or n1>n2<n3 than t = (m+1/2)constructive

2n

If n1<n2>n3 or n1>n2<n3 than t = (m+1/2)destructive

4n

Summary

Constructive interference – pathlength equals m Destructive interference – pathlength equal m 2

If n1<n2<n3 or n1>n2>n3 than t = mconstructive

2n

If n1<n2<n3 or n1>n2>n3 than t = mdestructive

4n

waves and optics formula velocity equals the product of the frequency and the wavelength formula:...

Documents

n2 sin f2the sin

optics formula formula

d sin f

incident angle

unitsindex of refraction

optics formulavelocity

image location

object location