Question

A crystal ball is $20cm$ in diameter with $\text{R. I}.=1.5$. If a lady is standing at $1.2m$ from the ball, calculate the distance between lady and her image formed by the crystal ball.

Answer 1

We have for refraction through a curved surface
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$


For refraction through surface (1)
$\frac{1.5}{v}-\frac{1}{-120}=\frac{1.5-1}{+10}--\left(1\right)$
$\Rightarrow v=36cm$

Image formed by surface (1) acts as a virtual object for surface (2).
Then, distance of virtual object from surface (2) $=36-20=16cm$

For refraction through surface (2),
$\frac{1}{v^{\prime }}-\frac{1.5}{+16}=\frac{1-1.5}{-10}--\left(2\right)$
$\Rightarrow v^{\prime }=6.9cm$
Thus, final image is formed $6.9cm$ to the right of the right surface of the crystal ball.
So,
Distance between lady and her image (D)
D = 120 cm + 2R + 6.9 cm =
D = 120 + 20 + 6.9 = 146.9 cm

Thus, the distance between lady and het image is 146.9 cm.