A ray of light in water (index n₁) is incident on its surface (with air) at the critical angle. Some oil (index n₂) is now floated on the water. The angle between the ray in the oil and the normal is: A) sin^-¹(1.00) B) sin^-¹(1/n₁) C) sin^-¹(1/n₂) D) sin^-¹(n₁/n₂) E) sin^-¹(n₂/n₁)

Question

Quizplus · Accepted Answer

When a ray of light passes from a denser to a rarer medium, it bends away from the normal, and when it passes from a rarer to a denser medium, it bends towards the normal. At the critical angle, the angle of incidence is such that the angle of refraction is 90 degrees, and the refracted Ray grazes along the surface of the denser medium. This angle of incidence at the critical angle is different for different pairs of media. When the oil is floated on the water, the angle between the ray and the normal increases, which means that the angle of incidence in the oil is greater than the critical angle. Therefore, the ray undergoes total internal reflection at the oil-water interface. The angle between the reflected ray in oil and the normal is the same as the angle of incidence in oil. Using the relation of Snell's law, sin i1/sin r1 = n2/n1, where i1 is the angle of incidence, r1 is the angle of refraction, n1 is the refractive index of the denser medium, and n2 is the refractive index of the rarer medium. At the critical angle, sin r1 = 1. For the ray that is reflected in the oil, the denser medium is the oil, and the rarer medium is the air. Hence, sin i1/sin r1 = n/n_{2. Therefore, sin i1 = n}/n_2.

A Ray of Light in Water (Index N1) Is Incident

A Ray of Light in Water (Index N₁) Is Incident