REFRACTION The bending of a ray of light as it passes from one medium to another is called refraction.

Reflection and Refraction at an Interface

The speed of light c in a material is generally less than the free-space velocity c of 3 x108 m/s. In water light travels about three-fourths of its velocity in air. Light travels about two-thirds as fast in glass. The ratio of the velocity c of light in a vacuum to the velocity v of light in a particular medium is called the index of refraction, n for that material.

nc

v

Light bends toward the normal when entering medium of higher index of refraction

Light bends away from the normal when entering medium of lower index of refraction

SNELL’S LAW

The ratio of the sine of the incident angle to the sine of the refracted angle is constant.

n1 sinθ1 = n2 sinθ2

 n1 = index of refraction of the incident medium

n2 = index of refraction of the second medium

Example A ray of light travels from air into liquid. The ray is incident upon the liquid at an angle of 30°. The angle of refraction is 22°.a. What is the index of refraction of the liquid?

n1 = 1

1 = 302 = 22

n1 sin 1 = n2 sin 2

2

112 sin

sin

n

n

22sin

30sin1 = 1.33

THIN LENSES Lenses are an essential part of telescopes, eyeglasses, cameras, microscopes and other optical instruments. A lens is usually made of glass, or transparent plastic.

A converging (convex) lens is thick in the center and thin at the edges.

A diverging (concave) lens is thin in the center and thick at the edges.

The two main types of lenses are convex and concave lenses. The focal length (f) of a lens depends on its shape and its index of refraction.

IMAGE FORMATION BY LENSES There are three principal rays to locate an image.

Ray 1. A ray parallel to the axis passes through the second focal point F2 of a converging lens or appears

to come from the first focal point F1 of a diverging

lens.

Ray 2. A ray which passes through the first focal point F1 of a converging lens or proceeds toward the

second focal point F2 of a diverging lens is refracted

parallel to the lens axis.

Ray 3. A ray through the geometrical center of a lens will not be deviated.

Principal Rays

A real image is always formed on the side of the lens opposite to the object. A virtual image will appear to be on the same side of the lens as the object.

23.7 a. Find the images formed by the following lenses

using the Ray Tracing method.

b. Write the characteristics of each image: -real or virtual, -larger, smaller or same size as object and-upright or erect.

No image is formed.

THE LENS EQUATION The lens equation can be used to locate the image:

1 1 1

d d fo i

Mh

h

d

di

o

i

o

The ratio M is called the magnification, ho is the object’s size and hi is the image size.

Where do is the object’s distance, di is the image distance and f is the focal length.

R radius of curvature

+ converging

- diverging 

f focal length

+ converging

- diverging

doobject distance

+ real object

+ real object

diimage distance

+ real images

- virtual images

hoobject size

+ if upright

- if inverted

hiimage size

+ if upright

- if inverted

23.8 A 5 cm tall object is located 30 cm from a convex lens of 10 cm focal length. a. Find the location and nature of the image.

do = 30 cm

f = 10 cm

dd f

d fio

o

30 10

30 10

( )= 15 cm, real

b. What is the height of the image?

ho = 5 cm

h

h

d

di

o

i

o

hd h

dii o

o

15 5

30

( )= - 2.5 cm, inverted

TOTAL INTERNAL REFLECTION

The incident angle that causes the refracted ray to lie right along the boundary of the substance is unique to the substance and is known as critical angle of the substance.

Total internal reflection is the phenomenon that involves the reflection of all the incident light off the boundary. It only takes place when both of the following two conditions are met:

- the light is in the more dense medium and approaching the less dense medium.

- the angle of incidence is greater than the so-called critical angle.

Critical Angle  n1 sin =  n2 sin

              =  n2 sin 90

    sin  =  n2 / n1

                                                      

An example of TIR is when a beam of laser light is directed into a coiled plastic. The plastic served as a "light pipe," directing the light through the coils until it finally exited out the opposite end. Once the light entered the plastic, it was in the more dense medium. Every time the light approached the plastic-air boundary, it was approaching at angles greater than the critical angle. The two conditions necessary for TIR were met, and all of the incident light at the plastic-air boundary stayed internal to the plastic and underwent reflection.

Other examples of Total Internal Reflection

   

Example Find the critical angle for an air-crown glass boundary.

ni= 1.52

nr= 1

sin c r

i

n

n

c r

i

n

n sin 1 sin

.1 1

152= 41˚