WBJEE · Physics · Ray Optics
A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius \(R=0.05 \mathrm{m}\) and refractive index \(n=1.5,\) placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose the nearest distance \(x\) from the cylinder is
- A \((3 \sqrt{3}-4) \times 10^{-2} \mathrm{m}\)
- B \((2 \sqrt{3}-2) \times 10^{-2} \mathrm{m}\)
- C \((3 \sqrt{5}-5) \times 10^{-2} \mathrm{m}\)
- D \((3 \sqrt{2}-3) \times 10^{-2} \mathrm{m}\)
Answer & Solution
Correct Answer
(C) \((3 \sqrt{5}-5) \times 10^{-2} \mathrm{m}\)
Step-by-step Solution
Detailed explanation
Given, radius \(R=0.05 \mathrm{m}\) Refractive index \(n=1 \cdot 5\) The critical angle, \(\sin c=\frac{1}{n}=\frac{1}{1 \cdot 5}\) \[ =\frac{10}{15}=\frac{2}{3} \] From above figure, \(\cos c=\frac{R}{R+X}\) \(\sqrt{1-\sin ^{2} c}=\frac{R}{R+X}\)…
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