Question

A glass is half-full of water, with a layer of vegetable oil (n = 1.47) floating on top. A ray of light traveling downward through the oil is incident on the water at an angle of 71.4°. Determine the critical angle for the oil–water interface and decide whether the ray will penetrate into the water.

Answer 1

Answer:

critical angle    = 64.79°

ray will not penetrate into the water

Explanation:

given details

refractive index of oil n1 = 1.47

refractive index of water n2= 1.33  

incident angle = 71.4 °

$\theta_c = sin^{-1}(\frac{n2}{n1})$

        = sin^{-1}(\frac{1.33}{1.47}

     critical angle    = 64.79°

incident angle > critical angle = reflection

incident angle < critical angle = refraction

In this case, 71.4 > 64.79 therefore it will undergo total internal reflection

therefore ray will not penetrate into the water