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Question
One end of a cylindrical glass rod (μ = 1.5) of radius 1.0 cm is rounded in the shape of a hemisphere. The rod is immersed in water (μ = 4/3) and an object is placed in the water along the axis of the rod at a distance of 8.0 cm from the rounded edge. Locate the image of the object.
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Solution
Given,
Radius (R) of the cylindrical rod = 1.0 cm
Refractive index (μg) of the rod = 1.5 = \[\frac{3}{2}\] Refractive index (μw) of water = 4/3 
\[\frac{\mu_g}{v} - \frac{\mu_w}{u} = \frac{\mu_g - \mu_w}{R}\]
As per the question, u = −8 cm.
Now,
\[\frac{3}{2v} - \left( - \frac{4}{3 \times 8} \right) = \frac{\frac{3}{2} - \frac{4}{3}}{1}\]
\[ \Rightarrow \frac{3}{2v} + \frac{1}{6} = \frac{1}{6}\]
\[ \Rightarrow v = \infty\]
Hence, the image will be formed at infinity (∞).
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