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A plastic hemisphere has a radius of curvature of 8 cm and an index of refraction of 1.6. On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object O. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately

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1.5 cm

3.75 cm

1.0 cm

2.5 cm

answer is D.

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Detailed Solution

Distance of image from the plane surface is:

$\begin{array}{l} x_{1} = \frac{4}{1 .6} = 2 .5 cm (d_{app} = \frac{d_{actual}}{μ}) for the curved side \frac{1 .6}{4} + \frac{1}{x_{2}} = \frac{1 - 1 .6}{8} \\ ∴ x_{2} \approx - 3 .0 cm \end{array}$

The minus sign means the image is on the object side

$∴ I_{1} - I_{2} = (8 - 2 .5 - 3 .0) cm = 2 .5 cm$

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