Question

A small object is embedded in a glass sphere $(\mu =1.5)$ of radius 5.0 cm at a distance 1.5 cm left to the centre. Locate the image of the object as seen by an observer standing to the left of the sphere?

Answer 1

We know,

$\frac{{\mu }_{air}}{v}-\frac{{\mu }_{glass}}{u}=\frac{{\mu }_{air}-{\mu }_{glass}}{R}$

Here,

The radius of the glass sphere $\left(R\right)$ is $5\text{cm}$, and the object distance is $u=-\left(5-1.5\right)=-3.5\text{cm}$

We put the values in the formula and get-

$\frac{1}{v}-\frac{1.5}{-3.5}=\frac{1-1.5}{-5}$

$\frac{1}{v}+\frac{3}{7}=\frac{-0.5}{-5}$

$\frac{1}{v}+\frac{3}{7}=\frac{1}{10}$

$\frac{1}{v}=\frac{1}{10}-\frac{3}{7}=\frac{7-30}{70}$

$\frac{1}{v}=\frac{7-30}{70}=\frac{-21}{70}$

Therefore, $v=\frac{70}{21}\approx 3\text{cm}$ from the surface of the glass sphere and the image of the object as seen by an observer standing to the left of the sphere will be at $2\text{cm}$left to the center.