Question

A concave spherical surface of radius of curvature $10cm$ separates two medium $x$ & $y$ of refractive index $4/3$ & $3/2$ 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 cm
• C. image is always virtual
• D. image is virtual if the object distance is less than 90 cm

Answer 1

Answer: (C)

Given : $R=-10$ cm $n_2=3/2$ $n_1=4/3$

Let the object is placed at a distance $x$ in front of the spherical surface i.e. $u=-x$

Using: $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

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

$⟹$ $v=\frac{-1.5x}{0.017x+1.33}$

$⟹$ $v<0$ i.e. the image formed is always virtual in nature.