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Chapter 30: Problem 11

Through what angle should you rotate a mirror so that a reflected ray rotates through \(30^{\circ} ?\)

Short Answer

Expert verified
The mirror should be rotated through \(15^{\circ}\).

Step by step solution

01

Identify the Problem

The problem asks for the angle through which you should rotate a mirror so that a reflected ray rotates through \(30^{\circ}\). It’s important to remember principle of reflection where the angle of incidence equals the angle of reflection. When a mirror is rotated through an angle, the reflected ray is rotated through twice that angle.
02

Apply the Reflection Principle

From the given problem, the reflected ray rotates through \(30^{\circ}\). Let's denote by \(x\) the angle through which the mirror should be rotated. We know that the angle of rotation of the reflected ray is twice that of the mirror. Therefore, we can write the equation as: \(2x = 30^{\circ}\).
03

Calculate the Mirror's Angle of Rotation

Now, solve for \(x\) in the equation \(2x = 30^{\circ}\). You can divide both sides of the equation by \(2\) to find the answer, which gives: \(x = 15^{\circ}\).

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