Refraction of light.

Refraction is the bending of light as it passes from one medium to another.

If light travels from air to glass, the incident ray is refracted towards the normal.

Light will always be refracted towards the denser medium.

If the incident ray enters the medium at right angles, refraction does not occur.

As the angle of incidence increases, so too does the angle of refraction.

Air

Glass Glass

The Laws of Refraction

The incident ray, the normal and the refracted ray all lie in the same plane.

The ratio of of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

Sin i = n ( a constant)

Sin r

Snell’s Law

The refractive index of a medium is the ratio of the sine of the angle of incidence to the sine of the angle of refraction when light travels from a vacuum into that medium.

sin i = n sin r

Medium n

Vacuum 1

Air 1.0003

Water 1.33 Glass 1.5

For any two media x and y xny = 1 ynx

Effects of refraction

Because of refraction, the depth of water in a pool or river will appear less.

Refraction will also cause an object placed in water to appear bent to an observer.

Real depth and apparent depth.

Refraction causes the true depth of a body of water to appear shallower than it actually is.

Light leaving a point from below is refracted at the surface of the water.

To an observer this light will appear to have come from a point nearer to the surface.

Refractive index n = real depth apparent depth

The speed of light.

In a vacuum, light travels at a speed of 3 x 108 m/s.

Refraction occurs because light changes speed as it travels from one medium to another.

The slower the speed of light in a medium, the greater the refractive index of that medium.

1n2 = c1

c2

Sin i = c1

Sin r c2

For any medium x,

nx = cair

cx

Critical angle.

The angle of refraction increases as the angle of incidence increases.

At some point the angle of incidence reaches a point where the angle of refraction is equal to 90°

The critical angle of a medium is the angle of incidence which produces an angle of refraction of 90°

C

r = 90°

Rarer medium

Denser medium

Total Internal Reflection.

If the angle of incidence is increased beyond the critical angle for a given medium, total internal reflection occurs.

No light escapes to the second medium, all of the light is ‘trapped’ inside the first medium.

Refractive index and critical angle

If light travels from a denser medium to a rarer medium, then the refractive index is given by,

aηb = sin i sin r

so aηb = sin C = sin C sin 90° 1If the second (rarer) medium is air, then the refractive index

becomes

xηa = sin C

Therefore the refractive index of a medium ‘x’ is given by,

aηx = 1 sin C

Example;The refractive index for

glass is 1.5, find the critical angle of glass.

η = 1.5 = 1/ sin C

Sin C = 1/ 1.5 = 0.6667

C = sin-1 0.6667 = 41.8°

Since the critical angle for glass is less than 42°, a ray of light that is incident at 45° will be totally reflected. A 45° prism may be used to turn a ray of light through 90°/180°

45°

45°

45°

Snell’s window.

Because of critical angle, it is found that only light striking the surface of water, within a circle of given radius may enter the water.

This is why underwater divers will only see a circular window of light when looking upwards.

This is often called Snell’s window.

P

d

r

C

Optical Fibres

Optical fibres are based on total internal reflection of light.

Light enters the fibre at an angle greater than the critical angle and is reflected where total internal reflection occurs again.

In this way light can be made to travel along the fibre without escaping.

Optical fibres are used in the telecommunications industry to transmit signals. They are also used in medicine to transmit light to inaccessible parts of the body, with endoscopes.