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Chapter 16: Problem 2218

For four different transparent medium $\mathrm{n}_{41} \times \mathrm{n}_{12} \times \mathrm{n}_{21}=$ (A) \(\left(1 / \mathrm{n}_{41}\right)\) (B) \(\mathrm{n}_{41}\) (C) \(\mathrm{n}_{14}\) (D) \(\left(1 / \mathrm{n}_{14}\right)\)

Short Answer

Expert verified
The correct answer is (A) \( \left(1 / \mathrm{n}_{41}\right) \).

Step by step solution

01

Understand the properties of refractive indices

Refractive index (n) is a dimensionless ratio that describes how light propagates through a medium. It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v): \( n = \frac{c}{v} \). When light travels from one medium to another, it changes its speed according to the refractive index of the second medium.
02

Determine the relationship between the given refractive indices

Let's examine the given refractive indices: n41, n12, and n21. We can rewrite these as \( n_{41} = \frac{n_4}{n_1} \), \( n_{12} = \frac{n_1}{n_2} \), and \( n_{21} = \frac{n_2}{n_1} \), where n1, n2, and n4 are the refractive indices of medium 1, medium 2, and medium 4 respectively.
03

Compute the product n41 × n12 × n21

Now, let's compute the product of the given refractive indices: \( n_{41} \times n_{12} \times n_{21} \). \[ n_{41} \times n_{12} \times n_{21} = \frac{n_4}{n_1} \times \frac{n_1}{n_2} \times \frac{n_2}{n_1} = \frac{n_4}{1} = n_{41}^{-1} \]
04

Compare the computed value with the given options

Comparing the computed value with the given options, we see that it matches option (A): \( n_{41} \times n_{12} \times n_{21} = \left(1 / \mathrm{n}_{41}\right) \) So, the correct answer is (A) \( \left(1 / \mathrm{n}_{41}\right) \).

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Most popular questions from this chapter

A Slit of width \(12 \times 10^{-7} \mathrm{~m}\) is illuminated by light of wavelength \(6000 \AA\). The angular width of the central maxima is approximately (A) \(30^{\circ}\) (B) \(60^{\circ}\) (C) \(90^{\circ}\) (D) \(0^{\circ}\)

The light waves from two coherent sources of same intensity interfere each other. Then what will be maxima intensity when minimum intensity is zero ? (A) \(4 \mathrm{I}\) (B) I (C) \(4 \mathrm{I}^{2}\) (D) \(\mathrm{I}^{2}\)

In young's double slit experiment the phase difference is constant between two sources is \((\pi / 2)\). The intensity at a point equidistant from the slits in terms of max. intensity \(\mathrm{I}_{0}\) is (A) \(3 \mathrm{I}_{0}\) (B) \(\left(\mathrm{I}_{0} / 2\right)\) (C) I_{0 } (D) \(\left(3 \mathrm{I}_{0} / 4\right)\)

The width of a single slit, if the first minimum is observed at an angle of \(2^{\circ}\) with a wavelength of light \(6980 \AA\) is \(\mathrm{mm}\) (A) \(0.2\) (B) \(2 \times 10^{-5}\) (C) \(2 \times 10^{5}\) (D) \(0.02\)

Mono chromatic light of wavelength \(399 \mathrm{~nm}\) is incident from air on a water \((\mathrm{n}=1.33)\) Surface. The wavelength of refracted light is \(\mathrm{nm}\) (A) 300 (B) \(\overline{600}\) (C) 333 (D) 443
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