In describing the propagation of light as a wave we need to understand:

wavefronts: a surface passing through points of a wave that have the same phase.

rays: a ray describes the direction of wave propagation. A ray is a vector perpendicular to the wavefront.

Reflection and RefractionWhen a light ray travels from one medium to

another, part of the incident light is reflected and part of the light is transmitted at the boundary between the two media.

The transmitted part is said to be refracted in the second medium.

reflected rayincident ray

The Law of ReflectionFor specular reflection the incident angle qi

equals the reflected angle qr:

qi = qr

The angles are measured relative to the normal, shown here as a dotted line.

Types of Reflection

• specular reflection

• diffuse reflection

• Mirrors reflect light and allow us to see ourselves.• O is the object or its coordinate• i is the image or its coordinate• p is the distance of the object to a mirror,

refracting surface or lens• q (or i) is the distance of the image to a mirror ,

refracting surface or lens• h is the object height• h’ is the image height• lateral magnification is the ratio of image height

to object height• an image is real if the light converges to form the

image in space• an image is virtual if the light appears to come

from a place where it cannot

Plan Mirrors

• Illustrating formation of an image by a plane mirror. • Since QR is common to both triangle PQR and

triangle P’QR and q is is the same angle at vertex P and vertex P’ the right triangles are congruent, and p = - q, alsoh = h’ or the lateral magnification (M) is +1.

• The image is upright, the same size and left-right reversed

Images from Mirrors

Spherical Mirrors• Definitions for the following terms

– Center of curvature (C)– Radius of curvature (R or r)– Principle Axis (or symmetry axis)– Vertex (V)

Spherical Mirrors• When parallel rays (e.g. rays from a distance

source) are incident upon a spherical mirror, the reflected rays intersect at the focal point f, a distance R/2 from the mirror.

The image formeation

R2

q1

p1

pq

M

• Sign Convention

Spherical Mirrors

• Convex mirrors: virtual images only

Spherical Mirrors

Focus and focal length

R2

q1

p1

R2

q11

fq 2R

f f1

q1

p1

Spherical Mirrors

Light inside a medium

Law of Refraction (Snell’s Law)

n1 sin1 = n2 sin2

sinc = n2 / n1

Critical AngleRequired

:• n1 > n2

• q1 > qc

Spherical Refracting Surfaces

Flat refracting surfaces and apparent depth

Rnn

qn

pn 1221

1221 nnqn

pn

qn

pn 21

pnn

q1

2

Thin Lenses

• Two spherical refracting surfaces back to back

• Thickness of lens is small (negligible)

Thin Lenses

1 2

11 1 n

p q R R

21 R1

R1

1nq1

p1

21 R1

R1

1nf1

f1

q1

p1

Thin Lenses

Thin Lenses

Converging and Diverging Lenses

Thin Lenses

Converging and Diverging Lenses

Principle Rays

Thin Lenses

Multiple Lens Systems

How do you locate the final image?

Where is the final image?

A- An object is placed 20 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?

• Solution:P=20 cm, f=10 cm

• the same size , real image

• An object is placed 5 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?

• Solution:P=5cm, f=10cm

q=-10 cm

Virtual image, as viewed from the right, the light appears to be coming from the (virtual) image, and not the object.

Magnification = +2

• An object is placed 8 cm in front of a diverging lens of focal length 4 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?

• Solution:P=8 cm, f=-4cm(concave)

The image is upright, virtual, smaller