Question

A convex lens of focal length 40 cm is held at a distance 12 cm coaxially above a concave mirror of focal length 18 cm. If the convex lens is replaced by a glass plate of thickness 6 cm, refractive index $\mu =\frac{3}{2}$ and gives rise to an image coincident with itself, then the value of d is equal to

• A. $26cm$
• B. $30cm$
• C. $40cm$
• D. $60cm$

Answer 1

The correct option is A $26cm$

When the ray from O passes through the slab of refractive index ($\mu$ ) , then there will be shift of point O to $I_1$ and then this point $I_1$ will act as source for the concave mirror.

Shift = $(1-\frac{1}{\mu })t$ $=(1-\frac{2}{3})6$

$⟹$ shift $=2cm$ i-e, the object will appear to look closer by

$2cm$.

Now as the final image is formed at point O itself, so the ray from point $I_1$ will retrace its own path (i-e, $I_1$ should be at $R$ of concave mirror).

So, $d-2+12=36$

$⟹d=26cm$