Question

A sphere 5 cm in diameter has a small scratch on its surface. When the scratch is viewed through the glass from a position directly opposite, where does the scratch appear and what is its magnification? Assume n = 1.5 for the glass.

Answer 1

Answer

given,

diameter of sphere = 5 cm

radius of sphere = -2.5 cm

refractive index for glass n₁ = 1.5

refractive index for air n₂ = 1

magnification of the glass = ?

now,

$\dfrac{n_1}{S} +\dfrac{n_2}{S'}= \dfrac{n_2-n_1}{R}$

$\dfrac{1.5}{5} +\dfrac{1}{S'}= \dfrac{1-1.5}{-2.5}$

$\dfrac{1.5}{5} +\dfrac{1}{S'}= \dfrac{0.5}{-2.5}$

                  S' = - 10 cm

magnification

 $m = \dfrac{-n_1S'}{n_2S}$

 $m = \dfrac{-1.5\times -10}{1\times 5}$

 m = + 3