Two plane mirrors are inclined to each other at an angle θ. A ray of light is reflected first at one mirror and then at the other. The total deviation of the ray is?

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Understand the Problem

The question is asking for the total deviation of a ray of light reflected between two mirrors inclined at an angle θ. We need to apply the principles of reflection and geometry to deduce the correct formula for total deviation.

Answer

The total deviation of the ray is $2\theta$.
Answer for screen readers

The total deviation of the ray is given by the formula: $$ D = 2\theta $$

Steps to Solve

  1. Understanding Reflection When a ray of light is reflected off a mirror, the angle of incidence is equal to the angle of reflection. This means that if the mirrors are inclined at an angle $\theta$, the behavior of the light ray will be influenced by this angle.

  2. Calculating Total Deviation The total deviation $D$ of a beam of light reflected between two mirrors inclined at an angle $\theta$ is given by the formula: $$ D = 2\theta $$ This is because the light reflects off each mirror, leading to a total change of twice the angle of inclination.

  3. Confirming the Formula The reasoning behind the formula comes from recognizing that each reflection changes the direction of the light by an angle equal to the angle between the mirrors, thus contributing to the total deviation of $2\theta$.

The total deviation of the ray is given by the formula: $$ D = 2\theta $$

More Information

This result shows how light behaves when reflected between two inclined mirrors. The angle of deviation is directly proportional to the inclination angle of the mirrors.

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