Question

A point object is situated at a distance of $36 \,cm$ from the centre of the sphere of radius $12\, cm$ and refractive index $1.5$. Locate the position of the image due to refraction through sphere.

• A. 24 cm from the surface
• B. 36 cm from the centre
• C. 24 cm from the centre
• D. Both (1) & (2)

Answer 1

Answer: (D)

$\mu_{1}=1$,
$\mu_{2}=1.5$
$u=-24\, cm$,
$R =+12 \,cm$
$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$
$\frac{1.5}{v}-\frac{1}{-24}=\frac{1.5-1}{+12}$
$v \rightarrow \infty$ becomes parallel to the principal axis.
On second face, $\mu_{1}=1.5, \mu_{2}=1, u \rightarrow \infty, R=-12 \,cm$
$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$
$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$
$\frac{1}{v}-\frac{1.5}{\infty}=\frac{1-1.5}{-12}$
$v=24\, cm$
Final image $\mu$ at $24 \,cm$ from the surface and from centre of sphere.