6 total internal reflection

Total Internal Reflection

glass

Reflection and refraction• Mirror reflects light

• Transparent medium refracts lightmirror

Which angle is larger?• A light ray is emerging from glass to air.

Which angle is larger, in glass or in the air ?

glassnormal

Or this?

This?AIR

glass

Which angle is larger?• A light ray is emerging from glass to air.

Which angle is larger, in glass or in the air ?

normal

Or this?

This?

Next

AIR

Critical Angle• For glass-air interface, the angle of refraction in

air > incident angle

glass

AIR

normal

Incident angle

Angle of refraction

Partial reflection

Which angle first?If the angle of incidence increases, which angle will reach 90o first, the angle of incidence or the angle of refraction?

A Angle of incidence (from glass)

B Angle of refraction (in the air)

Next

AIR

Critical angle (2)• When we increase the angle of incidence (i), the

angle of refraction (r) increases until ......

AIR

glassglass

AIR

glass

AIR

glass

i

r

normal

AIR

glass

Critical angle (3)• when the angle of refraction is 90o, the incident

angle is called the critical angle (C).

AIR

glass

r90o

normal

iC

sin 90o

sin C

Critical angle (4)• For glass-air interface, the critical angle is 42o.

• At critical angle, angle of refraction is 90o, so, by the laws of refraction,

n =sin rsin i

=1

n x sin C = 1

sin C =1n

What is the critical angle...… for water-air interface?

The refractive index of water is 1.33

sin C =1n

1 ÷ 1.33 = 0.75

sin-1 0.75 = 48.8o

=> C = 48.75o

For glass, the refractive index is 1.5;

C = sin-1 (1÷1.5)Critical angle = 41.81o

Critical angle (5)

sin C =1n

For water, the refractive index is 1.33;

C = sin-1 (1÷1.33)Critical angle = 48.75o

1n

C = sin-1 ( )

What if ...… the angle of incidence (from glass) is larger than the critical angle?

A The angle of refraction will become

smaller again.

B There will be no refracted ray.

C The light ray will be reflected the

same way back.

Next

Total internal reflection (1)• When the light ray (from water) is emerging at

the critical angle, the refracted ray will be along the interface.

water

AIR

alongalong

Total internal reflection (2)• When the incident angle is larger than the

critical angle, total internal reflection will occur (at the interface).

water

AIR

Next

Total internal reflection (3)• View under water!!

water

AIR

Total internal reflection (4)• Fish-eye view

You see

total internal

reflection here

You see the sky here

through refraction

You seewater waves

here

total internalreflection here

total internalreflection here

skywaves

waves

Can you explain the ...• fish-eye view by drawing light rays?

water

Yes

Fish eye view (1)

water

Central hole, shows thesqueezed view of the sky

totally internallyreflected ray

Fish eye view (2)• When a diver or fish looks upward under water,

part of the water surface looks like a mirror, except the central hole.

• So, the light entering the water from above the surface is squeezed into a cone of angle 2C

2C

water

What is C ?

C is critical angle

Revisit the fish eye view• Do you remember which part has refraction and

which part has total internal reflection?

total internalreflection here

sky(refraction here)

What did you learn?

• Critical angle

• Total internal reflection occurs when a light ray tries to escape from water (or glass) to air at an angle of incidence larger than the critical angle at the interface.

• Fish eye view is an example of total internal reflection and refraction.

1n

C = sin-1 ( )