Answer:
2.325 mm
Explanation:
n₁ = Refractive index of glass = 1.55
n₂ = Refractive index of air = 1
radius of the circular cross section = R = -0.05 m
h₀ = 1.5 mm
p = 0.05 m
[tex]\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}\\\Rightarrow q=\frac{1}{\frac{n_2-n_1}{Rn_2}-\frac{n_1}{pn_2}}\\\Rightarrow q=\frac{1}{\frac{1-1.55}{-0.05}-\frac{1.55}{0.05}}\\\Rightarrow q=-0.05\ m[/tex]
Magnification
[tex]M=\frac{h_i}{h_0}\\\Rightarrow M=\frac{-n_1q}{n_2p}\\\Rightarrow M=\frac{-1.55\times -0.05}{1\times 0.05}=1.55[/tex]
So, image length
[tex]h_i=h_0M\\\Rightarrow h_i=1.5\times 1.55 = 2.325\ mm[/tex]
∴ Length of line is seen by someone looking vertically down on the hemisphere is 2.325 mm
