Chapter 24, Problem 1RQ

To determine

The image distance for a plane mirror.

Answer to Problem 1RQ

The image distance for a plane mirror is equals the object distance.

Explanation of Solution

The ray incident along normally to the mirror gets reflected directly back along the normal. So it appears to have originated behind the mirror on the normal. The light ray that strikes the mirror at an angle $\varphi$ to the normal is reflected at an equal angle and appears to come from somewhere behind the mirror along the dashed projection of the outgoing ray.

The two projected paths cross behind the mirror at point $t$, the image position. The two right triangles have a common side $x$ and an equal angle $\varphi$. Hence the triangles are congruent. and all their angles and sides are equal. This means that the object distance $d$ and the image distance $d$ are the same.

Conclusion:

Therefore, the image distance for a plane mirror is equals the object distance.