Question

A point object is situated at a distance of $36cm$ from the centre of the sphere of radius $12cm$ 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)

${\mu }_1=1$,
${\mu }_2=1.5$
$u=-24cm$,
$R=+12cm$
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1.5}{v}-\frac{1}{-24}=\frac{1.5-1}{+12}$
$v\to \infty$ becomes parallel to the principal axis.
On second face, ${\mu }_1=1.5,{\mu }_2=1,u\to \infty ,R=-12cm$
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1}{v}-\frac{1.5}{\infty }=\frac{1-1.5}{-12}$
$v=24cm$
Final image $\mu$ at $24cm$ from the surface and from centre of sphere.