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Critical angle from the speed of light, or the time light takes, in two media

This type of question, asked 3 times: May 2022 S1, 19 Apr 2026 S2, 19 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    42
    The speed of light in two media M1 and M2 are 1.5×1081.5 \times 10^8 m/s and 2×1082 \times 10^8 m/s respectively. If the light undergoes total internal reflection, the critical angle between the two media is

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  2. Question 2

    19 Apr 2026 S2

    139
    Light travels a distance 'x' in time 't0t_0' in air and '4x4x' in time 't1t_1' in another denser medium. The critical angle for this medium is

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  3. Question 3

    19 May 2026 S1

    140
    A ray of light takes time 'tt' to travel a distance 'dd' in air and it travels a distance '4d4d', in time 'TT' in a certain medium. If T=8tT = 8t, the critical angle for the pair of media is [sin⁡(π6)=0.5,sin⁡(π4)=12,sin⁡(π3)=32,sin⁡(π2)=1]\left[\sin\left(\dfrac{\pi}{6}\right) = 0.5, \sin\left(\dfrac{\pi}{4}\right) = \dfrac{1}{\sqrt{2}}, \sin\left(\dfrac{\pi}{3}\right) = \dfrac{\sqrt{3}}{2}, \sin\left(\dfrac{\pi}{2}\right) = 1\right]

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