Waves and boundaries for SQA Higher Physics
This page covers the following topics:
2. Refractive index
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.
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 = n₂sinθ₂, where n₁ = incident index, n₂ = refracted index, θ₁ = angle of incidence, θ₂ = 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.
A light ray hits the boundary of a glass prism inside of it at an angle of 50°. 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 = 41.8°.
Since the angle of incidence is 50°, 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.
Refraction is the change in direction of a ray at a boundary between two transparent materials due to their different densities.
Explain what happens to a light ray moving through air when it is transmitted through glass.
Glass is denser than air, therefore when the light ray is transmitted through glass, it will slow down. Therefore, refraction will occur as the light ray will change direction by bending towards the normal.
A light ray is transmitted from water through to air. Given that the two angles are 28˚ and 34˚, explain which is the angle of incidence and which is the angle of refraction.
Water is denser than air, so when the light ray moves from water through to air, it speeds up and bends away from the normal due to refraction. Since it bends away from the normal, the angle of refraction must be greater than the angle of incidence. Therefore, the angle of incidence = 28˚ and the angle of refraction = 34˚.
An optical fibre of refractive index 1.4 is placed in water of refractive index 1.3. A light ray is travelling through the optical fibre and reaches the end of it. Given that the angle of incidence at the end of the optical fibre is 38°, calculate the angle of refraction as the ray enters the water to 3 significant figures.
Using Snell's Law, 1.3 × sin(38°) = 1.4 × sinθ.
sinθ = (1.3 × sin(38°))/1.4
θ = 34.9° (to 3 significant figures)
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