JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Geometrical Optics

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In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle

6 0^{\circ}

at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid

n = \frac{x}{4}

. The value of

x

is ______.
(Given refractive index of glass

= 1.5

)

Answer: 27

Solution

When the refracted ray grazes along face AC, the angle of refraction is

9 0^{\circ}

. Applying Snell's law at the AC interface:

n_{glass} sin 6 0^{\circ} = n sin 9 0^{\circ}

. Substituting:

1.5 \times \frac{3}{2} = n \times 1

, giving

n = \frac{3 3}{2}

. Since

n = \frac{x}{4}

, we have

\frac{x}{4} = \frac{3 3}{2}

, so

x = 63 = 108

. Wait, let me recalculate:

x = 33

, so

x = 9 \times 3 = 27

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer

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