Index of Refraction

Index of refraction of a medium is defined in terms of the speed of light in this medium

v

cn

In general, the speed of light in any material is less that its speed in vacuum.

v1 T = 1 , v2 T = 2

1 2

Hence

1

2

2

1

2

1

n

n

v

v

reflection and refraction

incident ray

reflected ray

refracted ray

1 ’1

2

angle of incidence

angle of reflection

angle of refraction

The law of reflection:

The reflected ray lies in the plane of incidence and the angle of reflection ’1 is equal to the angle of incidence ’

’1 = 1

The law of refraction:

The refracted ray lies in the plane of incidence and the angle of refraction 2 is related to the angle of incidence 1 by

n1 sin 1 = n2 sin 2

the law of reflection and the law of refraction

1

C

D

A

A’

’1

AC

AD

AC

C'A1sin 1'sin

11 '

2

B

1

2

v

v

C'A

AB

2sinACAB

1sinACC'A

2

1

n

n

2

1

1

2

n

n

sin

sin

1222 sinnsinn

ADC'A

Prism and Dispersion

Index of refraction of a material is a function of the wavelength

50

60

deviation angle

angle

dispersion angle

seeing objects

In order to be seen, an object must send light from each of its points in many directions. The eye collects some of the light emitted from a point allowing the brain to interpret the location of the point.

In some situations diverging rays are interpreted as originating from a single point creating an image of a point.

plane mirror

If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are reflected by the mirror, the rays or their extensions meet at a point to form an image.

object(real)

image(virtual)

s s’

reflecting surface

image(real)

s s’

object(virtual)

spherical mirror

If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are reflected by the mirror, the rays or their extensions meet approximately at a point to form an image.

O(object) parallel ray

(object) chief ray

(object) normal ray

(image) normal ray(image)

focal ray

(image) chief ray

(image) parallel rayC

F principalaxis

I

(object) focal ray

the mirror equation: O

C

I

0

s’

h

h’

s

R

's

s'sR

Rs

'h

h

R

2

s

1

's

1

from geometrical considerations:

R's'ss'sssR

'ss2R'ssR

f

1

For a concave mirror the focal length is positive and for a convex mirror the focal length is negative.

thin spherical lens

If the rays are emitted from a point (real object) or converge to a point (virtual object), after they are refracted by the lens, the rays or their extensions meet approximately at a point to form an image.

O(object) parallel ray

(object) chief ray

Fo

I

(object) focal ray

(image) focal ray

(image) parallel ray

Fi

(image) chief ray

thin lens equation

O

Fo

I

Fi

h

h’

s s’

f

's

s

'h

h

f's

f

fss's'fs

s'sfs'fs f

1

's

1

s

1

positive object’s position positive image position

lens maker's equationR1>0

R2<0

n0

n

The focal length of a thin-lens is determined by the curvatures of the two surfaces, the index of refraction of the lens material, and the index of refraction of the surrounding medium

210 R

1

R

11

n

n

f

1

Magnification

Object

Image

The magnification is defined as the ratio of the image height to the object height.

Mhh

'

s

's

h

s h’

s’

Fo

Fi

If the orientation of the image is the same as that of the object, a positive value is assigned to the magnification.

For an inverted image the magnification is negative.

angular magnification

The angular magnification (magnifying power) of an instrument is defined as the ratio of the "angular size" of the final image and the "angular size" of the observed object.

m '

N

example: magnifying glass

h

h’ ’

s

s

Nm

N

'h'

Ns

Nh

s

N

N

h

s

N

vision

cornea

retina

lens

Fo

Fi

If the object is between the near and the far point of the eye, its lens the eye muscles adjust the focal length of the lens to form a real image on the retina.

two thin lenses in contact

I1

F1o

F1i

F2o

F2i

O1

111 f

1

's

1

s

1

O2

222 f

1

's

1

s

1

1s

's2 's1

s

2s's

11 f

1

's

1

s

1

21 f

1

's

1

's

1

11 f

1

f

1

's

1

s

1

The system of two close lenses behaves like a single lens with a focusing power equal to the sum of the focusing powers of each lens separately.

compound microscope

objective

eye piece

L

specimen

'

m ef

'h h

L

ff

Lh

eo eo

2

ff

L

angular magnification

The objective produces the first (real) image almost at the focal point of the ocular. The eye piece form the final (virtual) image between the near and the far point of the observer’s eye.

L

h

Keplerian telescope

The objective produces the first (real) image almost at its focal point and the focal point of the ocular. The eye piece form the final (virtual) image between the near and the far point of the observer’s eye.

h’

angular magnification

'

m ef

'h

of

'h

e

o

f

f