Question

Image of an object is seen in a plane mirror, the distance from the mirror to the image depends on:
A. The distance of the observer from the mirror
B. The distance of the object from the mirror
C. The distance of both the observer and the object to the mirror
D. The thickness of the mirror

Answer 1

Hint: The radius of curvature of plane mirrors is infinite. Use the relation between radius of curvature and focal length to determine the focal length of the plane mirror. Use the mirror formula to determine the relation between image distance and object distance.

Complete step by step answer:
We know that the radius of curvature of the plane mirror is infinite. As we know the focal length of the mirror is half the radius of curvature of the mirror. Since the radius of curvature of the plane mirror is infinite, the focal length of the plane mirror is also infinite. We have the mirror formula relating focal length, object distance and image distance,
\[\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}\]
Here, f is the focal length, u is the object distance and v is the image distance.

Since the focal length f of the plane mirror is infinite, we can write,
\[\dfrac{1}{\infty } = \dfrac{1}{u} + \dfrac{1}{v}\]
\[ \Rightarrow \dfrac{1}{u} = - \dfrac{1}{v}\]
\[ \therefore v = - u\]
Therefore, the image distance is equal to the object distance for the plane mirror. The negative sign indicates that the image and object are on the opposite sides of the mirror.

From the above equation, we can say that the image distance depends only on the object distance. Therefore, the correct answer is option B. The distance from the mirror to the image does not depend on the distance of the observer from the mirror. Therefore, the option A is incorrect. The thickness of the mirror may affect the image for spherical lenses (not mirrors) because the refraction of light can be affected by the thickness of the mirror. Therefore, the option D is incorrect.

Hence, the only correct answer is option B.

Note: In mirrors, the image is formed due to reflection of the light ray from the mirror. Therefore, the thickness does not affect the image position. To answer this question, the crucial point to remember is the focal length of the plane mirror. The focal length of the spherical mirrors remains constant.