A mark placed on the surface of a sphere is viewed through glass from a position directly opposite. If the diameter of the sphere is 10 cm and refractive index of glass is 1.5, the image would be at
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -20 cm
A mark is on one surface of the glass sphere and is viewed from the opposite side, so refraction occurs at a single spherical surface.
Use the formula:
$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$
Given:
- Refractive index of glass $\mu_1 = 1.5$
- Refractive index of air $\mu_2 = 1$
- Diameter $= 10 \text{ cm} \Rightarrow$ object distance $u = -10 \text{ cm}$
- Radius $R = -5 \text{ cm}$ (center on object side)
Substitute:
$\frac{1}{v} - \frac{1.5}{-10} = \frac{1 - 1.5}{-5}$
$\frac{1}{v} + 0.15 = \frac{-0.5}{-5} = 0.1$
$\frac{1}{v} = 0.1 - 0.15 = -0.05$
$v = -20 \text{ cm}$