Refraction of Light. 2211 sinsin nn

A light beam going through a slab of glass:

12

12 sinsin

nn

31

24 sinsin

nn

23

12

1

1

24 sinsin

nn

nn

14

http://www.physics.uoguelph.ca/applets/Intro_physics/refraction/LightRefract.html

Frequency and wavelength at refraction.• As light travels from one medium to

another, its frequency does not change

– Both the wave speed and the wavelength do change

– The wavefronts do not pile up, nor are created or destroyed at the boundary, so f must stay the same

1

2

2

1

2

1

2

1

//

nn

ncnc

vv

21 ff 2

2

1

1

vv

Higher index of refraction corresponds to shorter wavelength

Color of the Sun from under water.

• The Sun looks yellow, since its radiation intensity has a maximum at = 550 nm, which is yellow light.

• Wavelength of this yellow light in water will be ’ = / nwater = /1.33 = 413 nm, which corresponds to violet light.

• Is the sun going to look violet from under water?

• Of course not! The only thing that matters is the wavelength inside your eye, which is defined by n of your vitreous humor.

Reflection and refraction indices - sparkling diamonds• For a light beam incident upon a boundary between two

transparent media at 90°:

221

221

)n(n)n(n

beamincident ofIntensity beam reflected ofIntensity

i

r

II

• Glass – n1 = 1.5, 04.0i

r

II

• Diamond – n1 = 2.4, 17.0i

r

II

A light beam coming from air, n2 = 1, and incident upon a surface of:

When light refracts into a material, where the index of refraction is lower, the angle of refraction is greater than the angle of incidence

The ray bends away from the normal

Snell’s law of refraction :

2211 sinsin θnθn We have 21 nn

If 1 is so large, sin1 > n2/n1, that also

211 sin nn

1/ 12 nn

What is 2 ?

???

Critical Angle• A particular angle of incidence

will result in an angle of refraction of 90°– This angle of incidence is

called the critical angle

211

2 forsin nnnn

c

For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary. This ray obeys the Law of Reflection at the boundary

Total internal reflection occurs only when light “attempts” to cross from a medium of higher index of refraction to a medium of lower index of refraction

• Critical angle - an angle of incidence which results in an angle of refraction of 90°

211

2 forsin nnnn

c

Glass and air5.1

1

1

2 nn 42)67.0(sin 1

c

Water and air33.11

1

2 nn 49)75.0(sin 1

c

Air and vacuum00029.1

1

1

2 nn 6.88c

• Critical angle - an angle of incidence which result in an angle of refraction of 90°

Air and vacuum00029.1

1

1

2 nn 6.88c

Cold air and hot air with 10% lower index of refraction

00029.100026.1

1

2 nn 6.89c It is still 0.4° from the surface!

Cold air and hot air with 10% lower index of refraction

00029.100026.1

1

2 nn 6.89c It is still 0.4° from the surface!

How do we get total internal reflection in the lab?

Would a flat-parallel slab work?

No, we need a prism with different angles at entrance and exit surfaces!

Those prisms are excellent reflectors. No silver coating needed!

Glass and air5.1

1

1

2 nn 42)67.0(sin 1

c

Ice and air3.1

1

1

2 nn 50)77.0(sin 1

c