Question

A plane wave travelling in a medium is incident on a plane surface separating this medium from a rarer medium. Draw a diagram to show refraction of the wave. Hence, verify Snell’s law.

Hint:

Snell’s law can be used to calculate the angle of refraction when light passes between two media with different refractive indices. The refractive index describes how much the light slows down in a given medium.

Answer 1

When a plane wave transitions between two media, its propagation direction alters due to differing light speeds. This change is termed refraction. Snell’s law quantifies the relationship between the angle of incidence in the denser medium and the angle of refraction in the rarer medium.

Diagram for Refraction:

The diagram below illustrates the refraction of a plane wave at a medium interface:

Incident plane wave in denser medium

↓

Angle of incidence (i)

Refraction occurs at the boundary

↓

Angle of refraction (r) in the rarer medium

Snell’s Law:

Snell’s law establishes the connection between the angle of incidence i and the angle of refraction r, incorporating the refractive indices of both media. The formula is:

Snell's Law Formula:
\( n_1 \sin(i) = n_2 \sin(r) \)

Variables are defined as:

• n1: refractive index of the denser medium,
• n2: refractive index of the rarer medium,
• i: angle of incidence,
• r: angle of refraction.

This equation is derivable from wave theory and the speed of light relationship across media. The refractive index n is defined as:

Refractive Index Formula:
\( n = \frac{c}{v} \)

where c is the speed of light in a vacuum and v is the speed of light in the specific medium.

Consequently, Snell’s law asserts that the ratio of the sines of the angles equals the ratio of the refractive indices.

Final Answer:

The refraction of a plane wave is governed by Snell’s law, which defines the relationship between the angles of incidence and refraction in two distinct media as:

Snell's Law:
\( n_1 \sin(i) = n_2 \sin(r) \)