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Total internal reflection at a prism face covered by a liquid or coating

This type of question, asked 4 times: 26 Jul 2022, 23 Jan 2026 S2, 24 Jan 2026 S1, 2 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    26 Jul 2022

    113
    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 AC. 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 )

  2. Question 2

    23 Jan 2026 S2

    15
    A prism of angle 75∘75^{\circ} and refractive index 3\sqrt{3} is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ____\_\_\_\_ . (sin⁡15∘=0.25\sin15^{\circ}= 0.25 and sin⁡25∘=0.43\sin25^{\circ}= 0.43 )

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  3. Question 3

    24 Jan 2026 S1

    6
    The exit surface of a prism with refractive index nn is coated with a material having refractive index n2\frac{n}{2}. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is ____\_\_\_\_

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  4. Question 4

    2 Apr 2026 S2

    16
    One side of an equilateral prism is painted by a transparent material of refractive index n2n_{2}. The refractive index of prism is 1.6 . The minimum value of n2n_{2} required for total internal reflection from painted face is ____\_\_\_\_ .

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