Light

Speed of Light vs Speed of Sound

As seen in the previous section, the speed of sound is 340 ms−1 in air. How does this compare to the speed of light ?

In the previous section, it was assumed that light travelled Instantaneously from place to place. This is not the case! Light travels incredibly quickly, but does have a fixed speed:-


Speed of Sound = 340 m s−1

Speed of Light = 300,000,000 m s−1 or 3x108 m s−1



As can be seen, light is much much faster than sound and over short distances can be assumed to be instantaneous.

Over large distances, however, the speed of light does have an effect. For instance, it takes 8 minutes and 20 seconds for light from the Sun to reach Earth.

Law of Reflection

When a wave 'hits' an object, the wave can change direction and 'bounce off' the object. This is known as Reflection.

There are two types of Reflection:-

1. Mirror Reflection - If the object has a very smooth surface, then all of the light is Reflected in the same way, making a mirror image.

2. Diffuse Reflection - If the object has a rough surface, then each ray of light will be Reflected in different directions, scattering the light. This is how most objects Reflect light.


When light hits a mirror, the ray of light is Reflected from its surface. The diagram below shows an example of this:-

Where:-

θi = Incident angle (angle going in) in degrees.

θR = Reflected angle (angle coming out ) in degrees.

In Optics, all angles are measured from the same place, a line called the normal. This is a line at a right angle to the surface of the mirror. Never measure an angle from the mirror itself.

By experiment, we can show that:-


" For a mirrored surface, The angle of incidence of a ray of light is equal to the angle of Reflection."


This is known as the law of Reflection.


Curved Reflectors

If the mirror is curved instead of flat (plane), then an unusual effect can be seen. Each part of the curved surface acts as a tiny plane mirror, following the law of Reflection. With the right shape, all of the light hitting the mirror will be focused to a single point.

This is how satellite dishes work. By Reflecting the signal all to the same point, the signal will be made stronger:-

Refraction

Refraction is the process by which a ray of Light changes direction (refracts) when passing between two different mediums (materials).

This direction change is caused by the light slowing down as it passes into the denser medium.

How to label Optics diagrams

The following diagram shows how to label all optics diagrams.

The most important line to draw on these diagrams in the Normal, a line drawn at right angles to the surface, which all angles are measured from.

Rectangular Block

The above diagram shows how the path of light is refracted by the rectangular block.

The diagram shows:-

1. Angle b is equal to angle c (they form a geometrical "Z angle").

2. Angle a is equal to angle d (as long as only two media are involved).


This is because:-

When the wave enters the more dense medium it slows down and is refracted towards the normal.

When the wave enters the less dense medium it speeds up and it is refracted away from the normal.


Semi-Circular Block

In the rectangular block, refraction occurs twice, but in a semi-circular block refraction occurs only once. This is because the light entering the curved side of the block enters along the normal, so no refraction occurs. Refraction only occurs at the plane glass boundary.


Triangular Prism

When a ray of white light passes through a Triangular Prism, the ray is refracted twice. The overall effect of these refractions is to cause the white light to be dispersed. This causes a spectrum to be observed.

Lenses

Convex Lens

Convex lenses are thicker in the middle than at the edges.

Convex lenses make the rays converge. The more curved the lens, the more refraction it causes.

Concave Lens

Concave lenses are thinner in the middle than at the edges.

Concave lenses make the rays diverge. The more curved the lens, the more refraction it causes.

How Lenses Refract Light

Lens are curved, which means that light entering at different positions will enter the lens at different angles to the Normal. This means they will be refracted by different amounts. The shape of each lens can be approximated to appear like two objects we have already seen, the rectangular block and triangular prism. The diagrams below show how these approximations can help explain the path of light through each lens:-

Power of a Lens

The the curvature of the lens affects the size of the focal Length. The more curved the lens, the shorter the focal length will be. This is used to great benefit within optics, especially as this allows for the correction of sight defects.

The power of a lens is used as a measure of how quickly the lens brings the light to a focus, and is described by the formula :-

P = 1 / f

Where:-

P - Power of a lens (Dioptres)

f - focal length (meters)

Note - In questions using this formula, it is possible to have negative power for a lens and therefore a negative focal length. Obviously a negative distance is not possible, the symbol is simply used to show lens type:-


Positive Power/Focal length - Convex Lens

Negative Power/Focal length - Concave Lens


Eye Defects

The diagram below shows the inside of a human eye, showing the major parts that allow vision:-

The key sections that allow vision are:-

Cornea - Transparent tough coat, most of refraction takes place here

Pupil - Gap at centre of Iris which allows light to enter the eye

Iris - Can alter the size of the Pupil to control how much light enters the eye

Lens - Flexible, has its shape altered by the ciliary muscles to focus light

Ciliary Muscles - Muscles that change the Lens shape to change the focal length of the Eye.

Retina - Lining of the back of the eye, covered in light sensitive cells

Optic Nerve - Carries signals from the retina to the brain


In order for clear, crisp vision, light must be focused correctly such that the light is brought to a focus point on the retina. as shown in the diagram below:-

Correcting Sight Defects

In modern society, the wearing of glasses is commonplace. Their invention seems to have occurred during the late 1200s, but no one is really sure by whom.

There is, however, anecdotal evidence written by Pliny the Elder in 79CE that the Emperor Nero used an Emerald to watch gladiatorial contests, possible to correct for short sightedness.

The diagram above shows the effect of short sight on the rays of light entering the eye. Uncorrected, the lens is too powerful and the light is brought to a focus short of the retina, giving a blurry image.

By using a concave lens to diverge the light before it enters the eye, the light can be made to focus correctly on the retina.

The diagram above shows the effect of long sight on the rays of light entering the eye. Uncorrected, the lens is too weak and the light is brought to a focus long of the retina, giving a blurry image.

By using a convex lens to converge the light before it enters the eye, the light can be made to focus correctly on the retina.


Total Internal Reflection

When light is incident on the curved side of a semi-circular block, no refraction occurs and the ray passes straight into the glass.

When light is incident on the flat side, refraction may occur. The following diagram gives the three possible outcomes for the incident ray of light:-

Note - the colour of the rays in the above diagram are for ease of labeling, not denoting colour of light.

θ1 = Ray of light is refracted and leaves the block

θc = Ray of light is refracted along the glass-air boundary (θrefraction = 90o )

θ2 = Ray of light is reflected back into the glass ( Total Internal Reflection )

The outcome we are interested in is θc - the Critical Angle.

For a ray of light:-

If the angle of incidence is less than the Critical angle, Refraction occurs

If the angle of incidence is greater than the Critical angle, Total Internal Reflection occurs


Optical Fibre

An optical fibre is made of two types of glass, with a dense glass core and a less dense outer cladding. When light enters the end of the fibre, it cannot escape and due to Total Internal Reflection, is reflected down the fibre and can only leave the glass at the far end.