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

Question

Infinity Learn · Accepted Answer

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

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

Ray optics

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Distance of image from the plane surface is:x1=41.6=2.5 cm dapp=dactualμ for the curved side 1.64+1x2=1−1.68∴x2≈−3.0 cmThe minus sign means the image is on the object side∴I1−I2=8−2.5−3.0 cm =2.5 cm

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