Waves and boundaries

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.

Refraction occurs due to the fact that different materials have different densities, which causes waves at the boundary between two transparent materials. Refraction is the change in direction that occurs at the boundary of the two materials due to this. 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.

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: n₁sinθ₁ = nβ‚‚sinΞΈβ‚‚, where n₁ = incident index, nβ‚‚ = refracted index, θ₁ = angle of incidence, ΞΈβ‚‚ = 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 90˚ 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 90˚ and can be calculate using: n = 1/sinC, where C = the critical angle.

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.

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 Ξ» and the angle at which the wave hits the gap ΞΈ is given by dsinΞΈ = nΞ», where n = the order number of the maximum and d = distance between adjacent grating lines.

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