Question

A concave mirror of radius of curvature $40\;cm$ forms an image of an object placed on the principal axis at a distance $45\;cm$ in front of it. Now if the system (including object) is completely immersed in water ( $\mu =1.33$ ), then:
(A) The Image will shift towards the mirror.
(B) The magnification will reduce
(C) The image will shift away from the mirror and magnification will increase
(D) The position of the image and magnification will not change.

Answer 1

Hint : To find the change in the image after immersion in water, we must remember that the concave and convex mirror produce an image by the phenomenon of reflection of light. Hence, from the laws of reflection, we can find the change in the image.

Complete Step By Step Answer:
Here the given data is;
Radius of curvature $R=40cm$
Object distance $u=45cm$
A concave mirror is a spherical mirror that is polished on the surface that is curved inward. Hence it converges the incident light falling on it following the laws of reflection.
Now, let us consider the arrangement in the air
The light rays coming from the object are parallel to the principal axis. The rays strike the mirror and get reflected back at some angle and the final image is formed between the focal length and the centre of curvature, which is smaller than the object.
Now, the law of reflection states that the angle of incidence is equal to the angle of reflection, no matter the medium through which the light is travelling as long as the medium is uniform.
Hence, when the whole setup is completely immersed in water, the medium changes as a whole. But the medium through which the light is travelling is uniform.
As the object distance does not change, the angle of incidence will also be the same. By the laws of reflection, the angle of reflection will also be the same.
Hence, the image of the object is formed at the same place and of the same size.
Hence, the correct answer is Option $(D)$ .

Note :
The fact to remember here is that light always travels in a straight line. It only bends when there is a change of medium in its path. Hence, for a lens or for a mirror, the light travels in a straight line as long as it is travelling in the same medium, be it air or water or vacuum. Also the focal length of a mirror is always constant.