Exercises: Polarization and Malus's Law
Explain in your own words what it means for light to be "polarized." Then state whether sound waves in air can be polarized, and give the reason for your answer.
Explain in your own words what it means for light to be "polarized." Then state whether sound waves in air can be polarized, and give the reason for your answer.
Unpolarized light of intensity $I_0 = 80\ \text{W/m}^2$ strikes an ideal polarizer. What is the intensity of the light that emerges? Is the emerging light polarized?
Unpolarized light of intensity $I_0 = 80\ \text{W/m}^2$ strikes an ideal polarizer. What is the intensity of the light that emerges? Is the emerging light polarized?
Polarized light of intensity $50\ \text{W/m}^2$ reaches an ideal polarizer. Find the transmitted intensity when the angle between the light's polarization direction and…
Polarized light of intensity $50\ \text{W/m}^2$ reaches an ideal polarizer. Find the transmitted intensity when the angle between the light's polarization direction and the polarizer's transmission axis is (a) $0^\circ$ and (b) $90^\circ$.
Polarized light of intensity $I_0 = 120\ \text{W/m}^2$ passes through an ideal polarizer whose axis makes an angle of $30^\circ$ with the light's polarization direction.…
Polarized light of intensity $I_0 = 120\ \text{W/m}^2$ passes through an ideal polarizer whose axis makes an angle of $30^\circ$ with the light's polarization direction. Then it passes through a second ideal polarizer whose axis is at $60^\circ$ to the first polarizer's axis. Find the intensity after each polarizer.
Emma holds two polarizing filters from a lab kit in front of a lamp. Unpolarized light hits the first filter. She rotates the second filter and records the transmitted…
Emma holds two polarizing filters from a lab kit in front of a lamp. Unpolarized light hits the first filter. She rotates the second filter and records the transmitted intensity:
| Angle between axes | Intensity after second filter (W/m²) |
|---|---|
| $0^\circ$ | 40 |
| $45^\circ$ | 20 |
| $90^\circ$ | 0 |
(a) What was the intensity of the lamp light before the first filter? (b) Show that the data follow Malus's law. (c) Predict the intensity at $60^\circ$.
Sunlight reflected from a lake is partially polarized horizontally. Explain how polarized sunglasses reduce glare from the water. State which direction the lenses'…
Sunlight reflected from a lake is partially polarized horizontally. Explain how polarized sunglasses reduce glare from the water. State which direction the lenses' transmission axes should point (vertical or horizontal) and why. Then explain what happens to the glare if Jayden tilts his head $90^\circ$.
Two ideal polarizers have axes at $90^\circ$ to each other, so no light gets through. Unpolarized light of intensity $I_0$ enters the first polarizer. A third ideal…
Two ideal polarizers have axes at $90^\circ$ to each other, so no light gets through. Unpolarized light of intensity $I_0$ enters the first polarizer. A third ideal polarizer is then inserted between them, with its axis at $45^\circ$ to the first.
(a) Find the final intensity as a fraction of $I_0$. (b) Explain why adding a filter can increase the light that gets through. (c) Find the angle for the middle polarizer that gives the largest final intensity, and compute that intensity as a fraction of $I_0$.
At a theater, Sofia watches a 3-D movie with passive polarized glasses. The projector sends two images with perpendicular polarizations, and each lens of the glasses…
At a theater, Sofia watches a 3-D movie with passive polarized glasses. The projector sends two images with perpendicular polarizations, and each lens of the glasses transmits only one of them.
(a) Explain how the glasses let each eye see a different image. (b) Sofia tilts her head by $30^\circ$. Using Malus's law, find the fraction of the intended image's intensity that reaches the correct eye and the fraction of the other image that leaks into it. (c) Explain why she sees ghosting. (d) Explain why an LCD screen viewed through polarized sunglasses can look dark when the glasses are rotated to certain angles.