Question

A sphere $(\mu =1.5)$ has a small bubble 6 cm from the center. Radius of the sphere is 10 cm. When seen normally from shorter side the bubble appears

• A. 3 cm below the surface
• B. 3 cm above the surface
• C. 7 cm inside the surface
• D. 4.6 cm below the surface

Answer 1

The correct option is A 3 cm below the surface

Refraction at Spherical surface

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

where, u, v, R are the x co-ordinates of the object, image and center respectively.

here,

$u=-4cm,R=-10cm,{\mu }_1=1.5,{\mu }_2=1$

$\Rightarrow \frac{1}{v}-\frac{1.5}{-4}=\frac{1-1.5}{-10}$

$\Rightarrow \frac{1}{v}=\frac{0.5}{10}-\frac{1.5}{4}$

$\Rightarrow \frac{1}{v}=\frac{-13}{40}$

$\Rightarrow v=-3.07cm$

Therefore, the bubble is 3cm below the surface