Question

A glass sphere $(\mu =1.5)$ of radius 20 cm has small air bubble 4 cm below its center. The sphere is viewed from outside and along vertical line through the bubble. The apparent depth of the bubble. The apartment depth of the bubble below the surface of sphere is (in cm)

• A. 13.33
• B. 26.67
• C. 15
• D. 30

Answer 1

The correct option is B 26.67

The observer sees the image due to refraction

at the spherical surface when the light

from the bubbeles goes from the glass

to the air.

Here, $u=-24em,R=-20cm,{\mu }_1=1\cdot 5,{\mu }_2=1$

$\frac{{\mu }_2}{\theta }-\frac{h_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{1}{v}-\frac{1\cdot 5}{U}=\frac{1-1.5}{-20}$

$\frac{1}{v}-\frac{1\cdot 5}{24}=\frac{0.5}{20}$

$\frac{1}{v}=\frac{1}{40}-\frac{1}{16}$

$\frac{1}{v}=\frac{-2+5}{80}$

$v=\frac{80}{3}$

$v=26\cdot 67cm$