Refraction of light

Generally, snell’s law for light travelling from medium 1 to medium 2 can be written as;
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The wave theory of light can be used to explain reflection and refraction of light. The light ray bends;

• towards the normal when it passes from air into glass.
• away from the normal when it passes from glass into air.

No refraction takes place if the incident light ray is along the normal.
At a boundary between two transparent substances, the light ray bends;

• Towards the normal if it passes into a more refractive substance
• away from the normal if it passes into a less refractive substance.
Measurements of the angles of incidence and refraction for different incident rays show that;
• the angle of refraction, r, at P is always less than the angle of incidence, i
• the ratio of sini/sinr is the same for each light ray. This is known as Snell’s law. The ratio is referred to as the refractive index, n, of glass

For a light ray travelling from air into a transparent substance;
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Notice that partial reflection also occurs when a light ray in air enters glass (or any other refractive substances)

Comparing ‘glass to air’ refraction with ‘air to glass’ refraction

The angle of refraction of the light ray emerging from the block is the same as the angle of incidence of the light ray entering the block. This is because the two sides of the block at refraction occurs are parallel to each other.

• If i₁ and r₁ are the angles of incidence and refraction at the point where the light ray enters the block, then the refractive index of the glass;
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• If i₂ and r₂ are the angles of incidence and refraction at the point where the light ray leaves the block, then because i₂ = r₁ and r₂ = i₂
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Refraction at a boundary between two transparent substances

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In general, total internal reflection can only take place if;

• the incident substance has a larger refractive index than the other substance
• the angle of incidence exceeds the critical angle

At the critical angle i_c, the angle of refraction is 90° because the light ray emerges along the boundary. Therefore; n₁sini_c = n₂sin90° where n₁ is the refractive index of the incident substance and n₂ is the refractive index of the other substance. Since sin90 = 1. Then;
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Dimensionless physical quantities

It is possible to obtain a quantity after mathematical manipulation that has no units attached to it. Such a quality is said to be dimensionless. E.g. the refractive index n of a medium maybe defined as;
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Since the two speeds have the same units, dividing them cancels the units and so n has no units and Is so becomes dimensionless.

Further notes

What is Snell’s law?

For any pair of media:
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…where θ, is the angle of incidence in the first medium and θ₂ is the angle of refraction in the second medium n₁ and n₂ are the refractive indexes of media 1 and 2 respectively.

Describe what happens to a ray of light when it passes from air through a denser medium and into air again.

When the ray of light enters the dense medium the refracted ray bends towards the normal, and when it leaves into the air it bends away from the normal. The incident ray and the emergent ray in the air are parallel.

If half the length of the block of the same block was used, will the value of the refractive index change? Why?

No, the refractive index of the glass will not change because it is the same material.
When light ray strikes the boundary between two media, the rays can undergo several physical processes e.g; reflection, refraction, etc. In this experiment, we are interested in refraction. We can define refraction as “the bending of light rays as they move from one medium to another of different optical density” We now know that light bends but in which direction does it bend? Is it away from the normal to the boundary or towards the normal? One physical parameter which can give a measure or degree of the bending after refraction is the index of refraction or simply the refractive index.