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.
The radii of curvature of the concave surfaces are \( R \), and the refractive index of the material is \( 1.5 \). Using the lens maker's formula for a spherical surface, the separation between the images of \( O \) formed by each surface is calculated. The distance between the two images is given by: \[\text{Distance between images} = 2R \left( 0.6R + \frac{9}{7} R \right) = 0.114 R\] Consequently, the separation between the images of \( O \) is \( 0.114R \).
