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A scuba diver uses his waterproof flashlight to shine a beam of light so that it strikes the surface of the water at an angle of incidence . Use Snell’s law to find the angle of incidence that would give an angle of refraction for the refracted ray to be directed right along the surface, and show that is the same as the critical angle for total internal reflection.
Using Snell's law, we can use n1Sinα=n2Sin β where α = Incidence angle, and β=angle of refraction. n1 and n2 are the indices of refraction for water and air.
Sinα=n2/n1 Sinβ For the refracted ray to be along the surface of water, β=90° and therefore Sinβ = 1
So, Sinα=n2/n1= 1/1.33 = 0.7519 => α=sin^-1 (0.7519) = 48.75°.
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