Question

A concave spherical surface of radius of curvature $10\text{cm}$ separates two medium $X$ & $Y$ of refractive index $\frac{4}{3}$ & $\frac{3}{2}$ respectively. If the object is placed along principal axis in medium $X$ then

• A. image is always real
• B. image is real if the object distance is greater than $90\text{cm}$
• C. image is always virtual
• D. image is virtual if the object distance is less than $90\text{cm}$

Answer 1

The correct option is C image is always virtual


Image is always virtual because rays go from rarer to denser medium.

Alternate solution:
Given: $R=-10\text{cm},n_2=\frac{3}{2},n_1=\frac{4}{3}$

Let $u=-x$
So, using, $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

Therefore, $\frac{3/2}{v}-\frac{4/3}{-x}=\frac{3/2-4/3}{-10}$

i.e. $v=\frac{-1.5x}{0.017x+1.33}$

This shows that $v<0$, i.e. image is always virtual in nature.