A ray of light is incident on a glass sphere of refractive index 3/2. What should be the angle of incidence in degrees so that the ray that enters the sphere does not come out of the sphere?

90.00

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90.0

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Solution

$∠ A B O = ∠ O A B = θ_{C}$
$sin θ_{C} = \frac{1}{μ} = \frac{2}{3}$

Applying Snell's law at A
$\frac{sin i}{sin θ_{c}} = \frac{3}{2}$
$sin i = (\frac{3}{2}) (\frac{2}{3}) = 1$
or i = $90$

Ans : $90^{\circ}$

Why this question?

Note: When a ray passes from an optically denser medium to an optically rarer medium, for a certian angle of incidence, there is no refraction and the ray undergoes total internal reflection. We call such angle of incidence as critical angle.

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