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Chapter 36: Problem 2895

The minimum angle of deviation of a prism of refractive index \(1.732\) is equal to its refracting angle. What is the angle of prism ? (A) \(45^{\circ}\) (B) \(30^{\circ}\) (C) \(60^{\circ}\) (D) \(40^{\circ}\)

Short Answer

Expert verified
The angle of the prism is \(A = 30^{\circ}\).

Step by step solution

01

Understand the Prism Formula

We will be using the Prism Formula to solve this problem, which relates the angle of the prism (A), the angle of minimum deviation (δ), and the refractive index (n) of the prism material. The Prism Formula is given as follows: \(n = \frac{\sin{(A + δ)/2}}{\sin{(A/2)}}\) Since the minimum angle of deviation (δ) is equal to the refracting angle (A), we have: \(n = \frac{\sin{(A + A)/2}}{\sin{(A/2)}}\)
02

Plug in the given refractive index

Now, we can plug in the given refractive index (1.732) in the Prism Formula and solve for the angle A. \(1.732 = \frac{\sin{(2A)/2}}{\sin{(A/2)}}\)
03

Simplify and solve for the angle

We now have an equation we can solve for the angle A: \(1.732 = \frac{\sin{A}}{\sin{(A/2)}}\) Let's multiply both sides by \(\sin{(A/2)}\) to isolate the sinus of A: \(1.732 \cdot \sin{(A/2)} = \sin{A}\) Now we can look for an angle A that satisfies this equation.
04

Check the given options

We will check each option to see which one satisfies the equation. (A) \(A = 45^{\circ}\) \(1.732 \cdot \sin{(45/2)} \approx 1.22\) (B) \(A = 30^{\circ}\) \(1.732 \cdot \sin{(30/2)} = 1.732\) Since option B satisfies the equation, the correct answer is: \(A = 30^{\circ}\)

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Most popular questions from this chapter

The minimum deviation produced by a glass prism of angle \(60^{\circ}\) is \(30^{\circ}\). If the velocity of light in vaccum is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Then what is the velocity of light in glass in \(\mathrm{m} / \mathrm{s}\) ? (A) \(2.72 \times 10^{8}\) (B) \(3.1 \times 10^{8}\) (C) \(2.9 \times 10^{8}\) (D) \(2.121 \times 10^{8}\)

A light ray is incident perpendicular to one face of \(90^{\circ}\) prism and is totally internally reflected at the glass-air interface. If the angle of reflection is \(45^{\circ} .\) We conclude that the refractive index \(\ldots\) (A) \(\mu>\sqrt{2}\) (B) \(\mu>(1 / \sqrt{2})\) (C) \(\mu<\sqrt{2}\) (D) \(\mu<(1 / \sqrt{2})\)

Angle of prism is \(\mathrm{A}\) and its one surface is silvered. Light rays falling at an angle at incidence \(2 \mathrm{~A}\) on first surface return back through the same path after suffering reflection at second silvered surface. What is the refractive index of material ? (A) \(\tan \mathrm{A}\) (B) \(2 \sin \mathrm{A}\) (C) \(2 \cos \mathrm{A}\) (D) \(\cos (\mathrm{A} / 2)\)

An equilateral prism deviates a ray through \(45^{\circ}\) for two angles of incidence differing by \(20^{\circ} .\) What is the \(\mathrm{n}\) of the prism? (A) \(1.467\) (B) \(1.573\) (C) \(1.65\) (D) \(1.5\)

A ray of light is incident normally on one of the faces of a prism of apex \(30^{\circ}\) and \(\mathrm{n}=\sqrt{2}\) What is the angle of deviation of the ray ? (A) \(45^{\circ}\) (B) \(30^{\circ}\) (C) \(15^{\circ}\) (D) \(60^{\circ}\)
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