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JEE Main 2022 (26 Jul, Shift 2) · Prism, Dispersion & Scattering

Prism, Dispersion & Scattering question from JEE Main 2022 (26 Jul, Shift 2)

Q55JEE Main 2022 · 26 JUL · SHIFT 2Difficult

Prism, Dispersion & Scattering

In the given figure, the face ACAC of the equilateral prism is immersed in a liquid of refractive index 'nn'. For incident angle 60∘60^\circ at the side ACAC, the refracted light beam just grazes along face ACAC. The refractive index of the liquid n=x4n = \frac{\sqrt{x}}{4}. The value of xx is ____________.

(Given refractive index of glass =1.5= 1.5)

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 27

  1. Grazing emergence at ACAC means the angle of incidence 60∘60^\circ is the critical angle for glass to liquid.
  2. μsin⁡60∘=nsin⁡90∘\mu \sin 60^\circ = n \sin 90^\circ
  3. n=1.5×32=334=274n = 1.5 \times \dfrac{\sqrt{3}}{2} = \dfrac{3\sqrt{3}}{4} = \dfrac{\sqrt{27}}{4}
  4. x=27x = 27
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