Electromagnetic Waves

Physics 202Professor Lee

CarknerLecture 21

PAL #20 EM Radiation Acceleration of lightsail craft

F = ma = prA a = prA/m pr = 2I/c I = Ps/4r2 = (3.9X1026)/((1.5X1011)2) = 1379 W pr = (2)(1379)/(3X108) = 9.2X10-6 N/m2

a = (9.2X10-6)(2.25X108)/5000 = 0.41 m/s2

Time to get to moon d = ½at2

t = (2d/a)½ = [(2)(3.8X108)/(0.41)] ½

t = 43054 sec ~ 12 hours Problems

Sunlight only pushes in one direction How do you stop or go back?

Gravity and inherited motion also important

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles (but the size stays the same)?

A) Goes inB) Goes outC) Stays put

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles and the surface area doubles?

A) Goes inB) Goes outC) Stays put

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the distance from the star doubles?

A) Goes inB) Goes outC) Stays put

Polarization

The plane containing the E vectors is called the plane of oscillation

Most light sources are unpolarized Any given wave has a

random plane of oscillation

Polaroid

Polaroid is a sheet of material that will only pass through the components of the E vectors in a certain direction

If you put a horizontal Polaroid sheet on top of a vertical Polaroid sheet no light gets through

Polarization and Intensity

The sum of all of the y components should be equal to the sum of all of the z components

I = ½ I0 This is true only when the incident light

is completed unpolarized What about polarized light hitting Polaroid?

Incident Polarized Light

For polarized light incident on a sheet of Polaroid, the resultant intensity depends on the angle between the original direction of polarization and the sheet

E = E0 cos

I = I0 cos2

For unpolarized light that pass

through two polarizing sheets, is the angle between the two sheets

Multiple Sheets

Sheet Angles

Means of Polarization

This alignment permits only the components in that direction to pass

The dust grains are partially aligned by the galactic magnetic field and so the light is partially polarized

Light can also be polarized by reflection

Reflection and Refraction When light passes from one medium to

another (e.g. from air to water) it will generally experience both reflection and refraction

Refraction is the bending of the portion of the light that does penetrate the surface

Geometry

Angles Angle of incidence (1): the

angle between the incident ray and the normal

Angle of reflection (1’):

Angle of refraction (2): the angle of the refracted ray and the normal

Laws Law of Reflection

Law of Refraction

n2 sin 2 = n1 sin 1

Where n1 and n2 are the indices of refraction of the mediums involved

Index of Refraction

Every material has an index of refraction that determines its optical properties

n is always greater than or equal to 1

Large n means more bending

General Cases

n2 = n1 2 = 1 e.g. air to air

n2 > n1 2 < 1 e.g. air to glass

n2 < n1 2 > 1 e.g. glass to air

Total Internal Reflection Consider the case where 2 = 90

degrees

For angles greater than 90 there is no refraction and the light is completely reflected

n1 sin c = n2 sin 90

c = sin-1 (n2/n1) This is the case of total internal

reflection, where no light escapes the first medium

Chromatic Dispersion

In general, n is larger for shorter wavelengths

Incident white light is spread out into its constituent colors

Chromatic dispersion with raindrops causes rainbows

Chromatic Dispersion

Polarization By Reflection Light reflected off of a

surface is generally polarized

When unpolarized light hits a horizontal surface the reflected light is partially polarized in the horizontal direction and the refracted light is partially polarized in the vertical direction

Brewster Angle

At B the reflected and refracted rays are perpendicular to each other, so

B + r = 90

B = tan-1 (n2/n1) If we start out in air n1 = 1 so:

B = tan-1 n

Next Time

Read: 34.1-34.6 Homework: Ch 33, P: 37, Ch 34, P:

7, 9, 10, 11, 12, 13, 15