/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 179 A beam of unpolarized light of i... [FREE SOLUTION] | 91影视

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Chapter 18: Problem 179

A beam of unpolarized light of intensity \(I_{0}\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intensity of the emergent light is [2013] (A) \(I_{0} / 2\) (B) \(I_{0} / 4\) (C) \(I_{0} / 8\) (D) \(I_{0}\)

Short Answer

Expert verified
The intensity of the emergent light after passing through both polaroid A and B is \(\frac{1}{4} I_{0}\).

Step by step solution

01

Unpolarized to polarized light (Polaroid A)

When unpolarized light passes through a polaroid filter, it becomes polarized and its intensity is halved. Therefore, the intensity of the light after passing through polaroid A is: \[I_{A} = \frac{1}{2} I_{0}\]
02

Applying Malus's law for Polaroid B

Malus's law states that the transmitted intensity of polarized light (I) after passing through a polarizer (in this case, B) is proportional to the square of the cosine of the angle (胃) between the planes of polarization. Mathematically, it can be written as: \[I = I_{A} \cos^2{\theta}\] Substitute the values of I鈧� and 胃 (45掳) in the equation: \[I = \left(\frac{1}{2}I_{0}\right) \cos^2{45^{\circ}}\]
03

Find the intensity after passing through Polaroid B

We know that \(\cos{45^{\circ}} = \frac{1}{\sqrt{2}}\). Substitute this value in the equation: \[I = \left(\frac{1}{2}I_{0}\right)\left(\frac{1}{2}\right)\]
04

Simplify the expression and find the correct answer

Calculating the intensity of the emergent light: \[I = \frac{1}{4} I_{0}\] Thus, the intensity of the light after passing through both polaroid A and B is \(\frac{1}{4} I_{0}\), which corresponds to option (B) in the given choices.

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Most popular questions from this chapter

In a displacement method using convex lens, two images are obtained for a separation of \(d\) between the positions of the lens. One image is magnified and the other is diminished. If \(m\) is the magnification of one image, the focal length of the lens is \((m>1)\) (A) \(d /(m-1)\) (B) \(m d /\left(m^{2}-1\right)\) (C) \(d /\left(m^{2}-m\right)\) (D) \((m-1) d\)

The plane face of plano-convex lens of focal length 20 \(\mathrm{cm}\) is silvered. This combination is equivalent to the type of mirror and its focal length is (A) convex, \(f=20 \mathrm{~cm}\) (B) concave, \(f=20 \mathrm{~cm}\) (C) convex, \(f=10 \mathrm{~cm}\) (D) concave, \(f=10 \mathrm{~cm}\)

In an experiment for determination of refractive index of glass of a prism by \(i-\delta\) plot, it was found that a ray incident at an angle \(35^{\circ}\), suffers a deviation of \(40^{\circ}\) and that it emerges at an angle \(79^{\circ}\). In that case which of the following is closest to the maximum possible value of the refractive index? \([2016]\) (A) \(1.6\) (B) \(1.7\) (C) \(1.8\) (D) \(1.5\)

A simple telescope, consisting of an objective of focal length \(30 \mathrm{~cm}\) and a single eye lens of focal length \(6 \mathrm{~cm}\). Eye observes final image in relaxed condition. If the angle subtended on objective is \(1.5^{\circ}\) then image will subtend angle of (A) \(6.5^{\circ}\) (B) \(7.5^{\circ}\) (C) \(0.3^{\circ}\) (D) \(2.5^{\circ}\)

When an object is placed at a distance of \(25 \mathrm{~cm}\) from a mirror, the magnification is \(m_{1} .\) The object is moved \(15 \mathrm{~cm}\) away with respect to the earlier position along principal axis, magnification becomes \(m_{2}\). If \(m_{1} \times m_{2}=4\), the focal length of the mirror is (A) \(10 \mathrm{~cm}\) (B) \(30 \mathrm{~cm}\) (C) \(15 \mathrm{~cm}\) (D) \(20 \mathrm{~cm}\)
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