A ray of light is incident from air on a glass plate having thickness √3 cm and refractive index √2. The angle of incidence of a ray is equal to the…
JEE Main 2023 — Physics Optics
2023integermedium
A ray of light is incident from air on a glass plate having thickness 3cm and refractive index 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}\mathrm{cm} . (given sin15∘=0.26)
Official previous-year question
Held on 25 Jan 2023 · Verified 6 Jul 2026.
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Solution
Let C be the critical angle.
Then, sinC=μ1, where, μ is the refractive index of glass.
So, sinC=21⇒C=45∘
As the angle of incidence is equal to the critical angle, so using Snell's law,
sinC=μsinθ
⇒21=2sinθ
⇒θ=30∘
Now, lateral displacement of the ray is
x=tsin(i−r)secr
⇒x=3sin(45∘−30∘)sec30∘
⇒x=3(0.26)(32)
⇒x=0.52cm
⇒x=52×10−2cm
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