Question

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at____ cm from the object.

Answer 1

Correct Answer: 200

Given:

\( \mu_1 = 1, \quad \mu_2 = 1.5, \quad R = 20 \, \text{cm}, \quad \text{Object distance} = 100 \, \text{cm} \)

Step 1: Apply the refraction formula

The governing formula is: \[ \frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R} \]

Step 2: Substitute given values

\[ \frac{1.5}{v} - \frac{1}{-100} = \frac{1.5 - 1}{20} \]

Step 3: Solve for \( v \)

\[ \frac{1.5}{v} + \frac{1}{100} = \frac{0.5}{20} \]

\[ \frac{1.5}{v} = \frac{0.5}{20} - \frac{1}{100} \]

\[ \frac{1.5}{v} = \frac{5}{100} - \frac{1}{100} = \frac{4}{100} \]

\[ v = \frac{1.5 \times 100}{4} = 37.5 \, \text{cm} \]

Step 4: Calculate the total distance from the object

Total distance = Object distance + Image distance = \( 100 \, \text{cm} + 37.5 \, \text{cm} = 137.5 \, \text{cm} \)

Final Answer:

\[ \boxed{137.5 \, \text{cm}} \]