Light travels a distance x in time t1 seconds in air, and a distance 10x in time t2 seconds in a certain medium. Find the critical angle of the medium.

sin⁻¹(10*t1 / t2)
sin⁻¹(t1 / (10*t2))
sin⁻¹(10*t2 / t1)
sin⁻¹(t2 / (10*t1))

Correct answer: sin⁻¹(10*t1 / t2)

Solution

Speed of light in air: c = x / t1. Speed of light in medium: v = 10x / t2. Refractive index of medium relative to air: n = c / v = (x/t1) / (10x/t2) = t2 / (10*t1). Critical angle theta_c satisfies sin(theta_c) = 1/n = 10*t1 / t2. Therefore theta_c = sin⁻¹(10*t1 / t2).

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