Chapter 24 & 25

Geometrical Optics &
Physical Optics

Polarization

Natural light

Linearly polarized wave

Polarizers

Transmitted Intensity for an Unpolarized Beam

(8)

Law of Malus

(9)

Example 11

Vertically polarized light with an intensity of passes through through a polarizer oriented at an angle to the vertical. Find the transmitted intensity of the light for (a) , (b) , (c) .

Solution:

Using Malus's Law :

(a)

(b)

(c)

Example 12

In the polarization experiment shown in the sketch, the final intensity of the beam is . What is the angle between the transmission axes of the analyzer and polarizer?

Solution:

Since we need to find the factor so that I = which is . Then set and solve for .

Example 13

Calculate the transmitted intensity for the following two cases: (a) A vertically polarized beam of intensity passes through a polarizer with its transmission axis at 60° to the vertical. (b) A vertically polarized beam of intensity passes through two polarizers, the first with its transmission axis at 30° to the vertical, and the second with its transmission axis at 60° to the vertical. In both cases, the final beam is polarized at 60° to the vertical.

Solution:

(a) Using the Law of Malus:

(b) Using the Law of Malus twice:

Example 14

Consider a set of three polarizers. Polarizer 1 has a vertical transmission axis, and polarizer 3 has a horizontal transmission axis. Taken together, polarizers 1 and 3 are a pair of crossed polarizers. Polarizer 2, with a transmission angle at 45° to the vertical, is placed between polarizers 1 and 3, as shown in figure. A beam of umpolarized light shines on polarizer 1 from the left. Is the transmission of light through the three polarizers (a) zero or (b) nonzero?

Solution:

(b) The transmission is nonzero.

On to Interference