A hemispherical paper weight contains a small artificial flower of transverse size 2 mm on its axis of symmetry at a distance of 4 cm from its flat surface. What is the size of the flower as it appears to an observer when he looks at it along the axis of symmetry from the top ? (Radius of the hemisphere is 10 cm. Index of refraction of glass = 1.5).

2.5 mm

Here $m=\frac{h_i}{h_0}=\frac{\mu_1 v}{\mu_2 u}$

From the question,

$\mu_1=1.5, \mu_2$ = 1

u = -6 cm, v = ?

∴ Using $\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}$ we have

$\frac{1}{v}-\frac{1.5}{-6}=\frac{1-1.5}{-10}$  ⇒  v = -5 cm

∴ $\frac{h_i}{h_0}=\frac{h_i}{2 ~mm}=\frac{1.5 \times-5}{1 \times-6}$ = 1.25

$\Rightarrow h_i$ = 2.5 mm