Question

A convex lens of focal length $30$ cm is placed in front of a luminous point object. The separation between the object and the lens is $90$ cm. A glass slab of thickness $t$ is placed between the object and the lens. A real image of the object is formed at the shortest possible distance from the object.

The refractive index of the slab is $\frac{t}{t-k}$. Find $k$.

Answer 1

The optical distance between lens and source is given by

$d-t+\frac{t}{\mu }$ where $d=90cm$

Now, we know that distance between real image and object is minimum when object is at $2f$ is the optical distance from lens.

$⟹d-t+\frac{t}{\mu }=2f$

$⟹90-t+\frac{t}{\mu }=60$

$⟹t(1-\frac{1}{\mu })=30=f$

$⟹1-\frac{1}{\mu }=\frac{f}{t}$

$⟹\mu =\frac{t}{t-f}$