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.
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Solution and Explanation
When a plane wave travels from one medium to another, its direction of propagation changes due to the difference in the speed of light in the two media. This phenomenon is called refraction. The angle of incidence in the denser medium is related to the angle of refraction in the rarer medium by Snell’s law.
Diagram for Refraction:
Below is the diagram showing the refraction of a plane wave at the boundary between two media:
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 relates the angle of incidence i and the angle of refraction r to the refractive indices of the two media. It is given by:
Snell's Law Formula:
\( n_1 \sin(i) = n_2 \sin(r) \)
where:
- n1 is the refractive index of the denser medium,
- n2 is the refractive index of the rarer medium,
- i is the angle of incidence,
- r is the angle of refraction.
This equation can be derived using the principles of wave theory and the relationship between the speed of light in the two media. The refractive index n is defined as:
Refractive Index Formula:
\( n = \frac{c}{v} \)
where c is the speed of light in vacuum and v is the speed of light in the medium.
Thus, Snell’s law ensures that the ratio of the sine of the angles is equal to the ratio of the refractive indices.
Final Answer:
The refraction of the plane wave can be described by Snell’s law, and the relationship between the angles of incidence and refraction in two media is given by:
Snell's Law:
\( n_1 \sin(i) = n_2 \sin(r) \)
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