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Chapter 8: Problem 24

Look at a light bulb through a piece of polaroid. Is the light polarized? Now insert a piece of cellophane (or your quarter- or half-wave plate) between the light bulb and the polaroid. Now is the light polarized? Reflect the light from a silvery metal, like a table knife. Is the reflected light polarized?

Short Answer

Expert verified
The light from a bulb is not polarized. Cellophane may cause interference effects, but the light remains unpolarized. Reflected light from metal can be polarized depending on the angle.

Step by step solution

01

Understanding Polarization

Light can be polarized by filtering it using a polaroid, which only allows light vibrating in a particular plane to pass through, or through reflection, where the angle of incidence affects the polarization.
02

Observing Light Through Polaroid

When you look at the light bulb through a polaroid, the light is typically not polarized because incandescent bulbs emit light in random directions. Therefore, it appears unchanged when viewed through a polaroid.
03

Inserting Cellophane or Wave Plate

When you insert a piece of cellophane or use a wave plate between the polaroid and the light bulb, the cellophane can cause interference effects, which may give the appearance of polarization due to altering the phase of different light paths. However, the light is not actually polarized in this step鈥攊t may just look differently due to color changes from interference.
04

Reflecting Light From a Metal Surface

Reflect the light from a smooth, metallic surface like a table knife. The reflected light can be polarized depending on the angle of incidence, according to Brewster's Law. Typically, at a specific angle, the reflected light will be polarized parallel to the surface, while light reflected from other angles will be less polarized.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polaroid Filter
A polaroid filter is a device that can filter light waves so that only waves oscillating in a specific plane can pass through it. It works kind of like a sieve for light. Normally, light from sources like light bulbs is unpolarized. This means it vibrates in many directions simultaneously. When you look at a light bulb through a polaroid filter, it doesn't appear different because the light is still mostly unpolarized due to its multi-directional nature. However, if light has been polarized or partially polarized from a different process, such as reflection, the polaroid filter can reveal the direction of its oscillation by blocking out other planes of light.
  • Polaroid filters are useful in sunglasses to reduce glare from surfaces like roads and water by blocking horizontally polarized light.
  • They are also used in photography to enhance contrast and color.
Brewster's Law
Brewster's Law helps us understand how light gets polarized upon reflection. When light hits a surface at a specific angle, known as the Brewster angle, the reflected light is perfectly polarized. This angle occurs when the refracted light inside the material and the reflected light are at 90 degrees to each other. At this angle, the reflected light is polarized parallel to the surface. This is especially noticeable on smooth, silvery surfaces, like a table knife.
The Brewster angle can be calculated using the formula:\[ \theta_B = \arctan\left( \frac{n_2}{n_1} \right) \]where \( n_1 \) and \( n_2 \) are the refractive indices of the two media involved.
  • This principle is used in photography and optics to control reflections and enhance the contrast of images.
  • Brewster's Law is particularly significant in designing anti-glare coatings for lenses.
Wave Plates
Wave plates, also known as retarder plates, are optical devices used to alter the polarization of light. They work by introducing a phase shift between two orthogonal components of the light wave, thereby modifying its state of polarization. When you place a cellophane or wave plate between the polaroid and a light source, it can create interference effects, making these alterations visible. Although this might appear like polarization, the light isn't truly polarized 鈥� it's more about how different colors emerge from the interference patterns caused by the phase difference.
  • Quarter-wave plates are used to convert linearly polarized light to circularly polarized light and vice versa.
  • Half-wave plates can rotate the polarization direction of linearly polarized light.
Wave plates play a crucial role in applications where precise polarization control is necessary, such as in laser systems and optical instrumentation.

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Most popular questions from this chapter

Suppose you have linearly polarized incident light with polarization along \(\hat{x}\) You desire linearly polarized light with polarization at 30 deg to \(\hat{x}\), i.e., along $$ \hat{e}=\hat{x} \cos 30^{\circ}+9 \sin 30^{\circ} $$ How can you obtain this transmitted field \((a)\) at the cost of some loss of intensity; \((b)\) without loss of intensity and without using any polaroids?

Moonlight and earthlight. When the moon appears half-full, the illuminated portion is scattering sunlight through about 90 deg to your eye. We know that for 90 deg scattering the blue sky is almost completely linearly polarized. Do you predict that half-moon-light is polarized? Do the experiment. Now think about how the earth looks from the moon at "half-earth." Is the earthlight polarized? (You can look for twenty-four hours while the earth turns.)

Circularly polarized light of intensity \(I_{0}\) is incident on a sandwich of three polaroids. The first and third polaroids are crossed, i.e., their easy axes are at 90 deg to one another. The middle polaroid makes an angle \(\theta\) with the axis of the first polaroid. Show that the output intensity is \(\frac{1}{2} I_{0} \cos ^{2} \theta \sin ^{2} \theta\)

Measuring the index of refraction by finding Brewster's angle. You need a light bulb (perhaps covered with a piece of cardboard with a hole to get a reasonably small source), a piece of glass, a table, a cardboard box or something to give a measurable location for your eye, and a single piece of polaroid. Lay the piece of glass flat on the table and look at the reflection of the bulb. (You will see two reflections, one from the front and one from the rear surface. If you wish to, you can eliminate the one from the rear surface by spraying the rear surface of the glass with black paint.) Vary the angles until the polaroid reveals that the reflected light is completely polarized. Measure the appropriate distances and obtain the index of refraction by the formula for Brewster's angle, \(\tan \theta_{B}=n .\) With this crude setup, you cannot measure to better than a few degrees, so that you probably cannot distinguish Brewster's angle for glass from that for a smooth surface of water.

Navigation by the Vikings. At high latitudes (say above the Arctic Circle) the magnetic compass is unreliable. The sun is also difficult to use for navigation; it may be below the horizon even at noon. Airline navigators then sometimes use a "twilight compass" that locates the sun's position below the horizon by means of the variation with direction of the polarization of the blue sky. The compass contains a piece of polaroid. Some natural crystals have properties similar to polaroid-one such substance is tourmaline; another is cordierite. When linearly polarized light is viewed through a cordierite crystal, the crystal is clear (with a yellowish tinge) when the polarization is along the axis of easy transmission, and the crystal is dark blue when the polarization is 90 deg to this axis. Such substances are called "dichroic." The Viking saitors of the ninth century navigated their ships without benefit of either magnetic compass or polaroid. At night they used the stars. In the day they used the sun, when it was not obscured by clouds. According to ancient Scandinavian sagas, the Viking navigators could always locate the sun, even when it was behind the clouds, by using magical "sun stones." It was long a mystery what these "sun stones" were. The mystery has probably been solved by a Danish archeologist, who knew
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