1.7 Polarization  (Page 7/20)

The angle between the axes of two polarizing filters is $45.0\text{°}$ . By how much does the second filter reduce the intensity of the light coming through the first?

Two polarizing sheets ${\text{P}}_1$ and ${\text{P}}_2$ are placed together with their transmission axes oriented at an angle $\theta$ to each other. What is $\theta$ when only $25\text{\%}$ of the maximum transmitted light intensity passes through them?

Suppose that in the preceding problem the light incident on ${\text{P}}_1$ is unpolarized. At the determined value of $\theta$ , what fraction of the incident light passes through the combination?

If you have completely polarized light of intensity $150{\text{W/m}}^2$ , what will its intensity be after passing through a polarizing filter with its axis at an $89.0\text{°}$ angle to the light’s polarization direction?

What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity $1.00{\text{kW/m}}^2$ to reduce the intensity to $10.0{\text{W/m}}^2$ ?

At the end of [link] , it was stated that the intensity of polarized light is reduced to $90.0\text{\%}$ of its original value by passing through a polarizing filter with its axis at an angle of $18.4\text{°}$ to the direction of polarization. Verify this statement.

Show that if you have three polarizing filters, with the second at an angle of $45.0\text{°}$ to the first and the third at an angle of $90.0\text{°}$ to the first, the intensity of light passed by the first will be reduced to $25.0\text{\%}$ of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

Three polarizing sheets are placed together such that the transmission axis of the second sheet is oriented at $25.0\text{°}$ to the axis of the first, whereas the transmission axis of the third sheet is oriented at $40.0\text{°}$ (in the same sense) to the axis of the first. What fraction of the intensity of an incident unpolarized beam is transmitted by the combination?

In order to rotate the polarization axis of a beam of linearly polarized light by $90.0\text{°}$ , a student places sheets ${\text{P}}_1$ and ${\text{P}}_2$ with their transmission axes at $45.0\text{°}$ and $90.0\text{°}$ , respectively, to the beam’s axis of polarization. (a) What fraction of the incident light passes through ${\text{P}}_1$ and (b) through the combination? (c) Repeat your calculations for part (b) for transmission-axis angles of $30.0\text{°}$ and $90.0\text{°}$ , respectively.

It is found that when light traveling in water falls on a plastic block, Brewster’s angle is $50.0\text{°}$ . What is the refractive index of the plastic?

At what angle will light reflected from diamond be completely polarized?

What is Brewster’s angle for light traveling in water that is reflected from crown glass?

A scuba diver sees light reflected from the water’s surface. At what angle will this light be completely polarized?

From his measurements, Roemer estimated that it took 22 min for light to travel a distance equal to the diameter of Earth’s orbit around the Sun. (a) Use this estimate along with the known diameter of Earth’s orbit to obtain a rough value of the speed of light. (b) Light actually takes 16.5 min to travel this distance. Use this time to calculate the speed of light.