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,

$$\frac{3}{2v}-(-\frac{4}{3\times 8})=\frac{\frac{3}{2}-\frac{4}{3}}{1}$$ 

$$\Rightarrow \frac{3}{2v}+\frac{1}{6}=\frac{1}{6}$$ 

$$\Rightarrow v=\mathrm{\infty }$$
Hence, the image will be formed at infinity (∞).