1.7 Polarization

Although we did not specify the direction in the example, let’s say the polarizing filter was rotated clockwise by $71.6 °$ to reduce the light intensity by $90.0 \%$. What would be the intensity reduction if the polarizing filter were rotated counterclockwise by $71.6 °$?

What happens at Brewster’s angle if the original incident light is already $100 \%$ vertically polarized?

Can a sound wave in air be polarized? Explain.

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Using the information given in the preceding question, explain why sunsets are red.

If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well. Why not?

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

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?

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

Show that if you have three polarizing filters, with the second at an angle of $45.0 °$ to the first and the third at an angle of $90.0 °$ to the first, the intensity of light passed by the first will be reduced to $25.0 \%$ 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.…

In order to rotate the polarization axis of a beam of linearly polarized light by $90.0 °$, a student places sheets $\text{P}_{1}$ and $\text{P}_{2}$ with their transmission axes at $45.0 °$ and $90.0 °$, 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 $30.0 °$ and $90.0 °$, respectively.

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

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

Cornu performed Fizeau’s measurement of the speed of light using a wheel of diameter 4.00 cm that contained 180 teeth. The distance from the wheel to the mirror was 22.9 km. Assuming he measured the speed of light accurately, what was the angular velocity of the wheel?

At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?

(a) Light reflected at $62.5 °$ from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

Unreasonable results Suppose light travels from water to another substance, with an angle of incidence of $10.0 °$ and an angle of refraction of $14.9 °$. (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

If a polarizing filter reduces the intensity of polarized light to $50.0 \%$ of its original value, by how much are the electric and magnetic fields reduced?

(a) On a day when the intensity of sunlight is $1.00 \text{kW}/\text{m}^{2}$, a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of $20.0 °$. Assuming the sunlight is unpolarized and the polarizers are $100 \%$ efficient, what is the initial rate of heating of the water in $° \text{C}/\text{s}$, assuming it is $80.0 \%$ absorbed? The aluminum bea…

Consider sunlight entering Earth’s atmosphere at sunrise and sunset—that is, at a $90.0 °$ incident angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle of refraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset. Now construct a problem in which you determine the angle of refraction for diff…

The light incident on polarizing sheet $\text{P}_{1}$ is linearly polarized at an angle of $30.0 °$ with respect to the transmission axis of $\text{P}_{1}$. Sheet $\text{P}_{2}$ is placed so that its axis is parallel to the polarization axis of the incident light, that is, also at $30.0 °$ with respect to $\text{P}_{1}$. (a) What fraction of the incident light passes through $\text{P}_{1}$? (b) What fraction of the incident light is passed by the combination? (c) By rotating…