Question

A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at

• A. 30 cm left
• B. infinity
• C. 1 cm to the right
• D. 18 cm to the left

Hint:

Negative \(v\) indicates virtual image on same side as object.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Refraction at spherical surface: \(\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}\).
Step 2: Detailed Explanation:
\(f = R/2 = 15\ \mathrm{cm}\), \(u = -15\ \mathrm{cm}\)
\(\frac{1.5}{v} - \frac{1}{-15} = \frac{1.5 - 1}{30}\)
\(\frac{1.5}{v} + \frac{1}{15} = \frac{0.5}{30} = \frac{1}{60}\)
\(\frac{1.5}{v} = \frac{1}{60} - \frac{1}{15} = -\frac{3}{60} = -\frac{1}{20}\)
\(v = -30\ \mathrm{cm}\) (left)
Step 3: Final Answer:
Image is 30 cm left.