Question

A small object stuck on the surface of a glass sphere $(\mu =1.5)$ is viewed from the diametrically opposite position.


Considering the proper sign convention, image position for observer will be

• A. $-2R$
• B. $+3R$
• C. $-4R$
• D. $-2.5R$

Answer 1

The correct option is C $-4R$

Incident ray originating from object $O$ is going towards right direction.

For observer,
$u=-2R;R=-R$

Here incident ray is travelling through medium of ${\mu }_1=1.5$ and observer is in air (${\mu }_2=1$)

And we know that,
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{1}{v}-\frac{1.5}{-2R}=\frac{1-1.5}{-R}$

$\Rightarrow \frac{1}{v}=\frac{-1}{4R}$

$\therefore v=-4R$

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

Why this question? Tip: While applying formula for refraction at spherical surface, be cautios to select the correct surface at which refractionis occuring. In this case, it is the surface close to observer (2nd surface).