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Waves and boundaries for AQA A-level Physics

Waves and boundaries

This page covers the following topics:

1. Reflection
2. Refraction
3. Refractive index
4. Absorption and transmission
5. Diffraction

Waves can be reflected at boundaries between two materials and obey the Law of Reflection. The Law of Reflection states that the angle of incidence of the wave should be equal to the angle of reflection of the wave. These angles are measured by taking the angle between the wave and the normal line, which is a line perpendicular to the surface of the boundary.

Reflection

Refraction is the change in direction of waves that occurs at a boundary of the two transparent materials. Refraction occurs due to the fact that different materials have different densities. A ray bends towards the normal when it is transmitted from a less dense through to a more dense material, since the denser material causes its speed to slow down. When the ray is passed from a more dense to a less dense material, it will bend away from the normal as it will speed up. Refraction appears as optical illusions to the human eye, as it cannot understand the concept of light changing direction.

Refraction

The refractive index is a measure of the extent that a ray will refract when moving from one medium to another. By Snell's Law, the refractive indices and the angles of incidence and refraction can be related using the following formula: nโ‚sinฮธโ‚ = nโ‚‚sinฮธโ‚‚, where nโ‚ = incident index, nโ‚‚ = refracted index, ฮธโ‚ = angle of incidence, ฮธโ‚‚ = angle of refraction. Since the refractive index of air is 1.0, when one of the mediums is air, the refractive index of the other medium can be shows as: n = sini/sinr, where i = angle of incidence and r = angle of refraction. The refractive index does not have units, as it is a ratio. Refraction cannot occur if the ray will be bent more than 90หš from the normal. In this case, the ray is reflected back into the denser medium by the Law of Reflection. This is called Total Internal Reflection and occurs when the angle of incidence is greater than the critical angle. The critical angle is the angle of incidence at which the angle of refraction is 90หš and can be calculate using: n = 1/sinC, where C = the critical angle.

Refractive index

When waves arrive at the boundary between two materials, they can be reflected, transmitted or absorbed. What happens to the wave energy depends on the following properties: the type of wave, the wavelength of the wave and the difference between the two media. The shorter the wavelength of the wave, the easier it is for it to be trasmitted.

Absorption and transmission

Diffraction is the change in direction of a wave that occurs when it goes through a gap or passes past an object. The diffraction effect is greatest when the size of the gap the wave is going through is similar to the size of the wavelength of the wave. A single slit produces an interference pattern of a broad central maximum and narrower and dimmer maxima to the sides. A grating is made up of many closely packed slits, and when a wave passes through it, diffraction occurs. When a wave passes through a grating, each slit acts as a coherent source of the wave. The relationship between the wavelength ฮป and the angle at which the wave hits the gap ฮธ is given by dsinฮธ = nฮป, where n = the order number of the maximum and d = distance between adjacent grating lines.

Diffraction

1

A light ray hits the boundary of a glass prism inside of it at an angle of 50ยฐ. Given that the refractive index of glass is 1.5, describe what happens.

To calculate the critical angle of glass, 1.5 = 1/sinC, so C = 41.8ยฐ.
Since the angle of incidence is 50ยฐ, it is greater than the critical angle, refraction will not occur.
Total internal reflection will occur and the light ray will be reflected back into the glass prism.

internal reflection

A light ray hits the boundary of a glass prism inside of it at an angle of 50ยฐ. Given that the refractive index of glass is 1.5, describe what happens.

2

State whether the following situation is an example of absorption or transmission of wave energy: the waves of the sea hitting the beach.

When the waves of the sea hit the beach, they are stopped by the sand, as most of the wave energy is taken by the sand. Therefore, this is an example of absorption.

State whether the following situation is an example of absorption or transmission of wave energy: the waves of the sea hitting the beach.

3

Define refraction.

Refraction is the change in direction of a ray at a boundary between two transparent materials due to their different densities.

Define refraction.

4

Given that the sum of the angle of incidence and the angle of reflection is 96หš, find the angle of incidence.

Let x = angle of incidence. By the Law of Reflection, angle of incidience = angle of reflection. Therefore, x = angle of incidence = angle of reflection. So, x + x = 96, thus 2x = 96. Therefore x = 48หš.

Given that the sum of the angle of incidence and the angle of reflection is 96หš, find the angle of incidence.

5

A light ray is reflected off a plane mirror at an angle of 52หš. What is the angle of incidence of the light ray?

By the Law of Reflection, the angle of incidence = angle of reflection. So, angle of incidence = 52หš.

A light ray is reflected off a plane mirror at an angle of 52หš. What is the angle of incidence of the light ray?

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