JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2023
- Medium
- Numerical
A ray of light is incident from air on a glass plate having thickness \(\sqrt{3} \,cm\) and refractive index \(\sqrt{2}\). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is \(.......\times 10^{-2}\) (given \(\sin 15^{\circ}=0.26\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(52\)
Step-by-step Solution
Detailed explanation
\(\sin c=\frac{1}{\sqrt{2}}\)
\(c=45^{\circ}\)
\(\sin c=\mu \sin \theta\)
\(\frac{1}{\sqrt{2}}=\sqrt{2} \sin \theta\)
\(\theta=30^{\circ}\)
Lateral displacement:
\(x=t \sin (i-r) \sec r\)
\(x=\sqrt{3} \sin \left(45^{\circ}-30^{\circ}\right) \sec 30^{\circ}\)
\(x=\sqrt{3}(0.26)\left(\frac{2}{\sqrt{3}}\right)\)
\(X=0.52\,cm\)
\(x=52 \times 10^{-2}\,cm\)
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