Homework Set 3From “Seeing the Light” Chapter 2:(starting page 68)

P22, P24, P26, PM4, From “Seeing the Light” Chapter 3:(starting page 101)

P1, P2, P3, P4Due: Monday, Feb 23

Dispersion of light• What is dispersion? And how it

comes about? • Optical Properties of diamonds

– Brilliance, fire, and flashes• Rainbow

– how does it happen? – Why everyone sees a different

rainbow?

Newton’s Discovery• Newton (at the age of 23) reached the

revolutionary conclusion that white light is not a simple, homogenous entity, as natural philosophers since Aristotle had believed.

• When he passed a thin beam of sunlight through a glass prism, he noted the oblong spectrum of colors: red, yellow, green, blue,violet– that formed on the wall opposite.

Dispersion• The index of refraction is not a constant!

It depends on the frequency of the light! This is because the light with different frequencies wiggles the charges with a different speed.

• Examples: water glass diamond

Red =656 nm 1.331 1.571 2.410Yellow =589 nm 1.333 1.575 2.418Blue =434 nm 1.340 1.594 2.450

THE SECRETTHE SECRETDifferent frequencies of Different frequencies of the light bend different the light bend different

amount as it passes amount as it passes through a dispersive through a dispersive

media.media.

THE SECRETTHE SECRETDifferent frequencies of Different frequencies of the light bend different the light bend different

amount as it passes amount as it passes through a dispersive through a dispersive

media.media.

Optical properties of diamonds

Why are the diamonds expensive?

• Diamonds has a large index of refraction (n=2.4) and has a small critical angle 24.5°. The diamond surfaces are cut so that most of light entering a diamond is eventually reflected back out the front brilliance!brilliance!– if you look from the back, the diamond

is black.

• Diamond is highly dispersive. So the white light is spread out into a broad spectrum the fire of the fire of diamondsdiamonds: beautiful colors: beautiful colors.

Flashes• Diamonds are cut with many

surfaces. When viewed from one angle, some light gets reflected from a particular surface and its color spreads out, reaching your eyes.

• As you turn the diamonds or yourself, some other rays reach your eyes with other paths. And this causes the flashflash ((sparklesparkle) of the diamonds.

Rainbows• Because of the dispersion of water,

droplets of water can break up the sun light into a spectrum rainbow

• How does this happen, precisely? – A light beam is dispersed twice through

raindrops and reflected once….

42°

• Since the red rays bend less than the blue, they have a steeper opening angle relative to the horizontal. – A math calculation shows that you see you see

the red rays from all those raindrops that the red rays from all those raindrops that lie at 42lie at 42° relative to the horizontal sun ° relative to the horizontal sun raysrays.

• The blue rays bend more, and have smaller opening angle relative to the horizontal. – You see the blue rays from all those

raindrops the lie at 40°.

Thus all rays from a rainbow comefrom different raindrops. And everybody sees a different rainbow!