Question

A point luminous object (O) is at a distance $h$ from the front face of a glass slab of width $d$ and of refractive index $\mu$. On the back face of a slab is a reflecting plane mirror. An observer sees the image of an object in the mirror as shown in the figure. Distance of image from front face as seen by observer will be :

• A. $h+\frac{2d}{\mu }$
• B. $2h+2d$
• C. $h+d$
• D. $h+\frac{d}{\mu }$

Answer 1

The correct option is A $h+\frac{2d}{\mu }$

As shown in figure glass slab will form the image of bottom i.e., mirror $M{M}^{\prime }$ at depth $(\frac{d}{\mu })$ from its front face.

So the distance of object $O$ from virtual mirror $m{m}^{\prime }$ will be $(h+\frac{d}{\mu })$. Now as a plane mirror forms image behind the mirror at the same distance as the object is in front of it, the distance of image $I$ from $m{m}^{\prime }$ will be $(h+\frac{d}{\mu })$ and as the distance of virtual mirror from the front face of slab is $(\frac{d}{\mu })$.

The distance of image $I$ from front face as seen by observer will be =$[h+(\frac{d}{\mu })]+\frac{d}{\mu }=(h+\frac{2d}{\mu })$