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

(a) To the left of the sphere and

(b) To the right of the sphere.

Answer 1

(a) For surface u = - 3.5 cm

${\mu }_1=1.5$

${\mu }_2=1$

$v_1=?$

$\frac{{\mu }_2}{v_1}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{1}{v_1}-\frac{1.5}{-\left(3.5\right)}=\frac{-0.5}{-5}$

$\frac{1}{v_1}=\frac{1}{10}-\frac{3}{7}$

$=\frac{7-30}{70}$

$=\frac{-23}{70}$

$v_1=\frac{-70}{23}\simeq -3$

So from centre, 2 cm towards left

(b) For Surface 2, u = - 6.5,

${\mu }_1=1.5$, ${\mu }_2=1$, $v=?$

$\frac{{\mu }_2}{v_1}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{1}{v}-\frac{1.5}{6.3}=\frac{1}{10}$

$\frac{1}{v}=\frac{1}{10}-\frac{3}{13}$

$=\frac{13-30}{130}$

$=\frac{-17}{130}$

$v=\frac{-130}{17}=-2.6$

So, 7.6 - 5 = 2.6 towards left from centre.