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.

Answer 1

Given,
Radius (R) of the cylindrical rod = 1.0 cm
Refractive index (μ_g) of the rod = 1.5 = \[\frac{3}{2}\] Refractive index (μ_w) 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 (∞).