If you are making a mirror for a big telescope (that uses visible light), how smooth should the glass be? In other words, irregularities in the glass should be no larger than (approximately!): a) 1 mm (10-3 m) b) 1 nm (10-9 m) c) 1 fm (10-15 m) d) there can be no irregularities at all

Wavelength & Frequency When light moves from a material of low index into a material with a higher index: The frequency increases and the wavelength is the same The frequency decreases and the wavelength is the same The frequency is the same and the wavelength increases The frequency is the same and the wavelength decreases Both frequency and wavelength change

Snell’s law

When a beam of light enters a piece of plexiglass, what will be its path? (np > 1)

The wave equation is time-reversal symmetric. A laser in air shines a beam of light that hits a diver, rightmost path. The diver has a laser pointer, and wants to hit the air laser. What direction should he point it? Or choose D: no direction will work.

As light goes from mat’l a to mat’l b, it bends as shown. A slab of transparent material with index nc is inserted. na<nb<nc What is the angle of the refracted ray now? Smaller Larger Same Depends on thickness of slab

Light is totally internally reflected at the interface between medium a and medium b. A slab of transparent medium c is placed over the interface. Light will now be transmitted into medium b: If it is not totally reflected at ac interface If slab c is thin enough never

Mirage: total internal reflection off hot air at the ground Mirage: total internal reflection off hot air at the ground. (nhot < ncold) Dispersion: different colors have slightly different index. Prisms, rainbows

Total internal reflection with microwaves! Frustration? Polarization? What direction of microwave polarization (i.e. E field) is blocked by a vertical metal fence? Vertical Horizontal

Polarization & Polarizers The component of the E field parallel to the pass direction passes. Ep = E0 cos  What intensity passes? Ip = I0 cos2  Malus’ Law The light that passes now has a polarization along the pass axis. Half of the intensity of unpolarized light goes through an ideal polarizer. What is unpolarized light???

Yes No If I “cross” two polarizers, no light gets through. Sam Student Says: “That makes sense: you’ve removed the horizontal component, and then you’ve removed the vertical component, so there’s nothing left.” If I add a third polarizer in between these two, Sam says: “You just added another filter to a filter system that already removes all the light. So no light gets through.” Is Sam right? Yes No

Polarization by reflection - Brewster’s angle Mnemonic This works because the reflection is caused by shaking of charges in the material. The shaking directions are the polarization directions in the material. But one shaking polarization can’t create a propagating wave in the reflected direction. Note: this is just a mnemonic. You also get polarization on internal reflection!

Circular & Elliptical Polarization Light Scattering - Clouds, “Steam” (which isn’t really steam), why sunsets are red Lastly: Huygen’s wavelets. Why does light refract? Bending of light is a straightforward consequence of change of wave speed.

Rainbows. Rainbows are parts of big circles Rainbows. Rainbows are parts of big circles. (Usually the ground prevents us from seeing the entire circle.) Where is the center of the circle? (Choose the best answer.) The sun A point 180° opposite to the sun Directly underneath the raincloud Why?

Rainbows. What color is on the outside? Red Violet