Determining the Angle of Refraction at the Water-Glass Interface

Understanding Snell's Law and Refractive Index

When light travels from one medium to another, it changes its direction. This phenomenon, known as refraction, can be quantified using Snell's Law. Snell's Law relates the angles of incidence and refraction of light as it passes through or from one medium to another. Mathematically, it is expressed as follows:

n1 sin θ1 n2 sin θ2

where:

n1 is the refractive index of the first medium (incident medium) θ1 is the angle of incidence n2 is the refractive index of the second medium (refractive medium) θ2 is the angle of refraction

Application to Water-Glass Interface

In this scenario, we are given that the light ray is incident on the water-glass interface at an angle of 30°. The refractive index of water, n1, is 1.333 and the refractive index of glass, n2, is 1.5. We need to determine the angle of refraction, θ2.

Step-by-Step Solution

Calculate sinθ1

Given θ1 30°, we find:

sinθ1 0.5

Apply Snell's Law

Substituting the known values:

1.333 sin 30° 1.5 sinθ2

0.6665 1.5 sinθ2

Solve for sinθ2

sinθ2 0.4443

Calculate θ2

Using the inverse sine function:

θ2 arcsin 0.4443 ≈ 26.5°

Conclusion

Therefore, the angle of refraction θ2 when a ray of light passes from water to glass at an incident angle of 30° is approximately 26.5°.

Additional Scenarios

As an extension, let's consider another scenario. Suppose the angle of incidence in a similar setup is 60°, with refractive indices of 1.3 for water and 1.5 for glass. Using Snell's Law again, we can find the angle of refraction.

1.3 sin 60° 1.5 sin r

sin r frac{1.3 times 0.866}{1.5} ≈ 0.751

r arcsin 0.751 ≈ 48.64°

Key Concepts and Definitions

Snell's Law: A fundamental principle in optics that describes the relationship between the angles of incidence and refraction when light passes through the interface of two different media.

Refractive Index: A measure of how much the speed of light is reduced when it passes through a medium. It is defined as the ratio of the speed of light in a vacuum to its speed in the medium.

Angle of Refraction: The angle measured with respect to the normal of the medium through which the incident light is passing.

This angle of refraction is an important concept in various fields, including astronomy, geology, and materials science, where the behavior of light in different mediums is critical.