Electromagnetic Waves

Physics 202Professor Vogel (Professor Carkner’s

notes, ed)Lecture 12

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

The new electric field becomes:E = E0 cos

Since I depends on E2 it becomes:I = I0 cos2

This is only true for polarized light For unpolarized light that pass

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

Multiple Sheets

Sheet Angles

Polarization By Reflection Light reflected off of a

surface is generally polarized This is why polarized

sunglasses reduce glare

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

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

Reflection is the portion of the light that does not penetrate the second medium but bounces off of the surface

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

Geometry

The normal line is a line perpendicular to the interface between the two mediums

Angles Angle of incidence (1): the

angle between the incident ray and the normal

Angle of reflection (1’): the angle of the reflected ray and the normal

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

Laws Law of Reflection

The angle of reflection is equal to the angle of incidence (1’ = 1)

Law of Refraction The angle of refraction is related to the

angle of incidence by:

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 = 1 for vacuum We will approximate air as n = 1 also

n is always greater than or equal to 1

Large n means more bending

General Cases

n2 = n1 No bending 2 = 1 e.g. air to air

n2 > n1 Light is bent towards the

normal 2 < 1 e.g. air to glass

n2 < n1 Light is bent away from the

normal 2 > 1 e.g. glass to air

Total Internal Reflection Consider the case where 2 = 90

degrees In this case the refracted light is bent

parallel to the interface For angles greater than 90 there is

no refraction and the light is completely reflected

2 > 90 when the incident angle is greater than the critical angle c

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

The index of refraction depends on the wavelength of light In general, n is larger for

shorter wavelengths Blue light bent more than

red

Incident white light is spread out into its constituent colors

Chromatic dispersion with raindrops causes rainbows

Chromatic Dispersion

Brewster Angle At a certain angle, known as the Brewster angle,

the reflected light is totally polarized At B the reflected and refracted rays are

perpendicular to each other, soB + r = 90

Since n1 sin B = n2 sin r we get

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

B = tan-1 n This is Brewster’s Law