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Chapter 8: Problem 25

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.

Short Answer

Expert verified
Use a polaroid to find Brewster's angle, measure the angle, and calculate the refractive index using \(n = \tan(\theta_{B})\).

Step by step solution

01

Set Up the Experiment

First, set the piece of glass flat on the table. Position the light bulb (or covered source) such that its light can reflect off the glass surface. You should be able to see the reflection on the glass.
02

Adjust Viewing Angles

Look into the reflection of the bulb using your eye. Adjust your viewing angle by moving around the glass until you find the angle where the reflection is maximally diminished using only one reflection (preferably the front surface reflection).
03

Use Polaroid to Polarize Light

With the polaroid sheet, rotate it while looking at the reflection. Continue to adjust your angle of viewing and the polaroid until you find the angle where the reflection is completely minimized or disappears, indicating the reflected light is completely polarized.
04

Measure Brewster's Angle

Once the reflection is completely polarized, measure the angle (胃_B) between the incident light and the normal to the surface. This is Brewster's angle.
05

Calculate Index of Refraction

Use the formula for Brewster's angle: \( an \theta_{B} = n\), where \(\theta_{B}\) is Brewster's angle. Solve for \(n\) (the index of refraction) by taking the tangent of the measured angle: \(n = \tan(\theta_{B})\).

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Key Concepts

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

Index of Refraction
The index of refraction is a vital concept in understanding how light behaves as it travels through different materials. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. Mathematically, it is represented as:
\[ n = \frac{c}{v} \]where:
  • \( n \) is the index of refraction.
  • \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \text{ m/s} \)).
  • \( v \) is the speed of light in the material.
The index of refraction determines how much light is bent or refracted when entering a different medium.
When light passes from one medium to another, its speed changes, which in turn changes the angle at which it travels. This is often why objects under water appear shifted from their actual position when viewed from above.
Knowing the index of refraction of a material is crucial for applications such as designing lenses for glasses, microscopes, and cameras, influencing how we focus and magnify images.
Polarization of Light
Polarization refers to the orientation of the oscillations of light waves. Typically, light waves vibrate in multiple planes. When light is polarized, it means the waves oscillate in a single plane. This concept is vital in understanding how Brewster's Angle works.
In everyday life, polarizing sunglasses use this concept to reduce glare. They allow light oscillating in a particular direction to pass through while blocking other directions, thereby reducing reflections from surfaces like water or roads.
During the experiment, using a polaroid sheet helps determine when the light is completely polarized. By rotating the polaroid while observing the reflection, one can find the position where the reflection diminishes. This occurs at the specific angle known as Brewster's angle. By minimizing reflections, we gain insights into the reflective properties of materials and how visible light interacts within them.
Optical Experiment
Optical experiments, like the one described in measuring Brewster's angle, help us understand the principles of light behavior. Experiments are set up to observe and measure physical phenomena in a controlled environment.
For Brewster's angle, the procedure requires aligning a light source with a piece of glass and using a polaroid to identify the angle where light is fully polarized. Despite the simple setup, it uses fundamental principles of light reflection and refraction.
  • A light source provides the necessary rays for reflection.
  • The glass acts as the reflecting surface where observations are made.
  • A polaroid is used to detect the angle of complete polarization.
By measuring the angles and using the relation \( \tan \theta_{B} = n \), where \( \theta_{B} \) is Brewster's angle, experimenters can calculate the index of refraction.
Such experiments highlight how theoretical concepts apply to real-world scenarios, enhancing our understanding of materials' optical characteristics.

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Most popular questions from this chapter

Phase relations in specular reflection of light from glass. We are trying to verify the relationships shown in Fig. 8.8. The experimental setup is as in Home Exp. 8,25, except that between the piece of glass lying on the table and the light we place a piece of polaroid with easy axis rotated at 45 deg to the horizontal. (Sugges tion: For a convenient mounting, put a little nonhardening putty or glazing compound on a microscope slide and stick the corner of the polaroid into the putty. The microscope slide can be the glass surface used for reflecting the light.) Suppose that when your eye is at the microscope slide and you are looking back at the light bulb through the first polaroid, the easy direction of the polaroid is "upper right to lower left." Keep analyzing the polarization of the reflected light as you vary the angle of incidence by changing the position of the slide or light bulb. You will find that near normal incidence the polarization of the reflected light is along "upper left to lower right." As you move the slide and approach Brewster's angle, the polarization remains linear, but it rotates toward the horizontal. It becomes horizontal at Brewster's angle and then continues to rotate in the same direction as you go beyond Brewster's angle toward grazing incidence; i.e., it becomes "lower left to upper right." Thus in going from normal to grazing incidence, the polarization rotates by \(90 \mathrm{deg}\), as predicted by Fig. 8.8. (At normal incidence, both components are equally well reflected, as they must be since they don't know which is which, so to speak. Therefore the polarization is at 45 deg. At grazing incidence, both components are almost completely reflected, so that they are equally well reflected. Therefore the polarization is at 45 deg.) It is interesting to notice that the polarization remains linear through all of this experiment. This means that there are no phase shifts other than 0 or 180 deg introduced between those components in the plane of incidence and those perpendicular to it. Thus the incident waves always experience a purely resistive load when they reflect. That is what we expect for reflection from a transparent medium.

What is the transmitted intensity for unpolarized light of intensity \(I_{0}\) incident on crossed polaroids with a half-wave plate between them, \((a)\) when the retardation plate's optic axis (say the slow axis) is parallel to the easy axis of one of the polaroids; (b) when the wave plate's optic axis is at 45 deg to one of the easy axes?

Optical activity. Suppose you send linearly polarized light through a length \(L\) of Karo corn syrup and find that, for \(L=5 \mathrm{~cm}\), red light is rotated by 45 deg. Now reflect the light that has passed through the syrup from a mirror and send it back through the syrup, so that the total length is \(10 \mathrm{~cm}\). (If you do the experiment, make the angle of reflection not quite \(180 \mathrm{deg}\); then look at the "image light bulb" through both the "real syrup" and the "image syrup." As a control experiment, you can look through the "image syrup" alone by moving your head.) Question: After the two traversals, is the linear polarization at 0 or 90 deg to the original direction?

Circularly polarized light of intensity \(I_{0}\) (intensity means energy fux per unit area per unit time; this is proportional to a photomultiplier's output current, for light at a given frequency) is incident on a single polaroid. Show that the output intensity (intensity of the light emerging from the rear of the polaroid) is \(\frac{1}{2} I_{0}\)

Linearly polarized light with polarization direction at angle \(\theta\) from \(\hat{x}\) is incident on a polaroid with easy axis along \(\hat{x} .\) The first polaroid is followed by a second polaroid with its easy axis along the direction of polarization of the original incident light. Show that if the input intensity is \(I_{0}\), the output intensity is \(I_{0} \cos ^{4} \theta\).
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