Question

A convex lens of focal length $f_1$ is placed in front of a luminous point object. The separation between the object and the lens is $3f_1$. 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.
a. Find the refractive index of the slab.
b. If a concave lens of very large focal length $f_2$ is placed in contact with the convex lens, find the shifting of the image.

Answer 1

a. For a convex lens, minimum distance between the object and image is $4f$ in which distance between the object and lens is $2f$ and between the lens and screen is $2f$,
Hence, shifting $=3f_1-2f_1=f_1$
$s=t\left[1\right(1/\mu \left)\right)\Rightarrow \mu =t(t-f_1)$
b. $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{(-f_2)};\frac{1}{v^{\prime }}-\frac{1}{u}=\frac{1}{F};u=-2f_1$
$\Rightarrow v^{\prime }=\frac{2f_1{f}_2}{f_2-2f_1}$
Shifting of image,
$s=v^{\prime }-v=\frac{2f_1{f}_2}{f_2-2f_1}-2f_1=\frac{4f_1^2}{f_2-2f_1}=\frac{4f_1^2}{f_2}$ (as $f_2>>f_1)$.