Question

A glass slab $(\mu =\frac{3}{2})$ is placed infront of a concave mirror as shown in the figure. At what distance $x$ should an object be placed to the left of the slab, such that the final image forms on object itself.

• A. $x=10\text{cm}$
• B. $x=15\text{cm}$
• C. $x=40\text{cm}$
• D. $x=30\text{cm}$

Answer 1

The correct option is C $x=40\text{cm}$


The normal shift produced by the slab $S=t(1-\frac{1}{\mu })$

Substituting the given data we get,

$S=15\times (1-\frac{1}{3/2})=5\text{cm}$

For the mirror, the object is placed at a distance $p=(x-5+15+10)\text{cm}$

If Image and object have to coincide , the position of the object as seen from the mirror, should appear to be at the centre of curvature of the mirror. So, as seen from the mirror, object is placed at the centre of curvature of mirror.

Position of object as seen from the mirror is , $x-5+15+10=60\text{cm}$

$\Rightarrow x=40\text{cm}$

Hence, option (c) is the correct answer.

Why this question? This question involves multiple concepts. It checks if the student can apply the concept of shift due to glass slab along with image formed by spherical mirrors.