Question:
Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:
Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:
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In problems involving concave refracting surfaces, use the lens maker's formula and consider the effects of both surfaces on the light to find the total separation between the images.
Updated On: Mar 24, 2025
- 0.214R
- 0.114R
- 0.411R
- 0.124R
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The Correct Option is B
Solution and Explanation
Let the radii of curvature of the concave surfaces be \( R \), and the refractive index of the material be \( 1.5 \). The separation between the images of \( O \) formed by each surface can be derived using the lens maker's formula for a spherical surface.
The distance between the two images is given by the formula:
\[
\text{Distance between images} = 2R \left( 0.6R + \frac{9}{7} R \right) = 0.114 R
\]
Thus, the separation between the images of \( O \) is \( 0.114R \).
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