As shown in Fig. E33.11
, a layer of water covers a slab of material X in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find (b) the angle the light makes with the normal in the air.

Verified step by step guidance

1. Identify the indices of refraction for the two slabs and air: n1 = 1.53 (Slab 1), n2 = 1.47 (Slab 2), and n3 = 1.00 (Air).
2. Use Snell's Law at the interface between Slab 1 and Slab 2: n1 * sin(θ1) = n2 * sin(θ2). Here, θ1 is the angle of incidence in Slab 1, and θ2 is the angle of refraction in Slab 2, which is given as 42 degrees.
3. Rearrange Snell's Law to solve for θ1: θ1 = arcsin((n2/n1) * sin(42 degrees)).
4. Use Snell's Law again at the interface between Slab 2 and Air: n2 * sin(θ2) = n3 * sin(θ3). Here, θ3 is the angle of refraction in Air, which we need to find.
5. Rearrange Snell's Law to solve for θ3: θ3 = arcsin((n2/n3) * sin(42 degrees)).

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another with a different index of refraction. This change in speed causes the light to change direction, which is described by Snell's Law. The angle of incidence and the angle of refraction are related to the indices of refraction of the two media involved.

Snell's Law

Snell's Law mathematically describes the relationship between the angles of incidence and refraction when light travels between two different media. It is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the indices of refraction of the first and second media, respectively, and θ1 and θ2 are the angles of incidence and refraction. This law is essential for calculating the angle of light as it exits a medium.

Index of Refraction

The index of refraction (n) is a dimensionless number that describes how much light slows down in a medium compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. Higher indices indicate that light travels slower in that medium, affecting the angle at which it refracts when transitioning to air or another medium.