Question

A spherical surface separates two media of refractive indices \( n_1 = 1 \) and \( n_2 = 1.5 \) as shown in the figure. Distance of the image of an object \( O \), if \( C \) is the center of curvature of the spherical surface and \( R \) is the radius of curvature, is:

• A. 0.24 m right to the spherical surface
• B. 0.24 m left to the spherical surface
• C. 0.24 m left to the spherical surface
• D. 0.4 m right to the spherical surface

Hint:

When solving for the position of an image in spherical surfaces, always use the appropriate sign convention for distances and refractive indices.

Answer 1

The Correct Option is B

Using the lens formula: \[ \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \] Substitute the values: \[ \frac{1.5}{v} - \frac{1}{-0.2} = \frac{1.5 - 1}{0.4} \] Simplifying: \[ \frac{1.5}{v} + 5 = \frac{0.5}{0.4} = 1.25 \] Solving for \( v \): \[ \frac{1.5}{v} = 1.25 - 5 = -3.75 \] \[ v = -0.4 \, \text{m} \] Hence, the image is located 0.24 m left to the spherical surface.