A light ray strikes a clean slab of ice of thickness 1.00 m at an angle of 45^ to the surface. It is then refracted into the ice at an angle of 30^ . Determine the time taken by the light ray to cross the slab. The speed of light in vacuum is 3 10^8 m s ⁻¹ .

Step-by-step solution

Angle of incidence, i = 90^ - 45^ = 45^ Angle of refraction, r = 30^ Refractive index of ice, = i r = 45^ 30^ = 1/ 2 1/2 = 2 Speed of light in ice, v = c = 3 10^8 2 m s ⁻¹ Distance travelled by light in the slab, L = d r = 1 30^ = 2 3 m Time taken, t = L v = 2 / 3 3 10^8 / 2 = 2 2 3 3 10⁻⁸ s t = 2 1.414 3 1.732 10⁻⁸ s 5.44 10⁻⁹ s