Reflection and refraction

Reading: Chapter 33, THE NATURE AND PROPAGATION OF LIGHT

Study guide: Chapter 33

  1. Nature of light / Huygen's principle

  2. Reflection from surfaces

  3. What's an image?

  4. Huygen's principle

  5. Refraction

Nature of light

sunlight through clouds

How we draw it: as straight lines--rays (as if particle like). (Eventually bending at boundaries.)

Huygen's pictured each point on a wavefront as a new source of waves. His picture is consistent with wave fronts that propagate with speed $c$.

(Waves spreading out far from a point source will get closer and closer to straight lines of wavefronts)


 

Reflections from a plane surface

Light reflecting from a smooth surface:

$\phi_1=\phi_2$. but Why?

Huygen's construction: Reflected wavelength (and frequency) should be the same.

Fermat's principle: equal angles of reflection can also be derived by assuming that light always takes the quickest path between two points (but going via the mirror...).

Light reflecting from a rough surface:

Images

Light is emitted (or reflects off) of each point on an object

Our eye/brain assumes straight line propagation of light.

Moving around a bit, we note light beams that all seem to be converging on the same point, and assume there's an object at the point of convergence.

With a mirror present, the rays appear to converge to points again, but at locations behind the mirror, at the location of a "virtual" image".



Why doesn't this happen with rough paper?

Refraction

Maxwell's equations said (in vacuum) $$c=\frac{1}{\sqrt{\epsilon_0}{\mu_0}}$$

But in other materials, we have a different dielectric constant $\epsilon\neq \epsilon_0$ and magnetic permeability $\mu\neq\mu_0$, $\Rightarrow$ a different speed for light. For visible wavelengths, the speed is generally slower than in a vacuum.

$$n=\frac{\text{speed of light in a vacuum}}{\text{speed of light in material}}$$

Glass: $n$=1.5...1.7
Water: $n=1.33$
Diamond: $n=2.4$
Air: $n=1.0003$

This causes a bending at interfaces:

Huygen's picture: (like lines of soldiers marching from pavement into mud...)

Fermat's picture: Quickest path for a lifeguard to troubled swimmer...

What about normal incidence?



Snell's law

sunlight through clouds

Notice that $\phi_1$ is the same as the angle that the direction of propagaton makes with the normal.

In medium 1 and medium 2, $\lambda_1\neq\lambda_2$ and wave speed $v_1\neq v_2$.What about frequency? How many waves pass A in one second?How many waves pass B in one second?

$$n_1\sin\phi_1=n_2\sin\phi_2$$Snell's law.

[Find the angle in glass...]

If light were a particle instead of a wave... Think about shooting BB's at water: In which medium is the speed of the BB faster? How do you think the trajectory would bend??

What is the maximum angle in air (or in general, in the medium with the smaller $n$)?

If $n_1\lt n_2$, come up with a general formula for the critical angle $\phi_c$: This is $\phi_2$ when $\phi_1$ is at that maximum angle...

What is the critical angle in the glass shown, when air is outside?





$$\phi_c =\arcsin(n_1/n_2)$$

A pipe for light:

 Fiber optic cables

Snell's law and swimming pools

Dispersion...

index of refraction is not exactly the same for different wavelengths.

What's the trend?

Because the sky is blue ...


But why??

E-M waves are given off by accelerating charges. (Waves in all directions, stronger perpendicular to acceleration).


What happens to another electron in the path of the wave?

Compare fast shaking (short wavelength) to slow shaking (long wavelength).

Which speed-of-shaking results in more (re)-radiation? (in all directions, but more perpendicular to acceleration...)

Image credits

Steve H, Sprengben, Pat Dalton, David Yu