Question

A concave spherical surface of radius of curvature $10$ cm separates two mediums $x$ and $y$ of refractive index $\frac{4}{3}$ and $\frac{3}{2}$ 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 $90$ cm
• C. Image is always virtual
• D. Image is virtual if the object distance is less than $90$ cm

Answer 1

The correct option is C Image is always virtual


Given,
$R=-10\text{cm},n_2=\frac{3}{2},n=\frac{4}{3}$
Let, the object be placed at a distance in front of the spherical surface,
i.e., $u=-x$
using $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$
Put the value here,
$\therefore \frac{\frac{2}{3}}{v}-\frac{\frac{4}{3}}{x}=\frac{\frac{3}{2}-\frac{4}{3}}{-10}$
$v=\frac{-1.5x}{0.017x+1.33}$
$v<0$ that is image is always virtual in nature.