Question

An object is placed at a distance of $10cm$ from the curved surface of a glass hemisphere of radius $10cm$. Find the position of the image from the flat surface.

• A. $26.67cm$
• B. $2.67cm$
• C. $2cm$
• D. $19.67cm$

Answer 1

Answer: (A)

$26.67cm$

For refraction at spherical surface,

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\frac{\frac{3}{2}}{v}-\frac{1}{u}=\frac{\frac{1}{2}}{10}$

$\frac{v}{\frac{3}{2}}=-20$

$v=-30$

Therefore image will be at 30 cm behind curved surface when seen from glass. From flat face it will be at (10+30 = 40) 40 cm in glass when it is observed from air.

So,

$d_{app}=\frac{d}{refractiveindex}$

$d_{app}=\frac{40}{\frac{3}{2}}$

$d_{app}=\frac{80}{3}$

$d_{app}=26.67cm$

Thus option A is correct.