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

Let, the object be placed at a distance $x$ in front of the spherical surface,
i.e., $u=-x$
Using, $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$
From the given data we have,
$\frac{\frac{3}{2}}{v}-\frac{\frac{4}{3}}{-x}=\frac{\frac{3}{2}-\frac{4}{3}}{-10}$

$\Rightarrow v=\frac{-1.5x}{0.017x+1.33}$

From the above expression we can conclude that $v<0$, that is image is always virtual in nature.

Hence, option $\left(c\right)$ is the correct answer.