Oscillations & Waves, Reflection & Refraction

In geometric optics, we only consider light travelling in straight lines.

• The direction light is travelling is represented by a ray (simply a line with an arrow on it)
• A beam of light can be represented by a collection of rays

Pinhole camera

By treating light as being made up of rays moving in straight lines, we can explain large-scale observations, such as eclipses, and small scale observations, such as how a 'pinhole camera' can produce a clear image. A pinhole camera can be made simply from a small cardboard box, with a small hole in one side, and the opposite side cut out and replaced by a semi-transparent material to act as a screen. The hole is 'pointed' at a bright object, and an inverted image is formed on the screen:

REFLECTION BY PLANE MIRRORS (‘plane’ = ‘flat’) (return to start of page)

Laws of reflection

There are two laws of reflection:
1. The incident ray, the reflected ray and the normal at the point of incidence are all in the same plane – hence, they can be drawn on a flat piece of paper, as in the above diagram
2. The angle of incidence equals the angle of reflection (i = r in the above diagram)
Real and virtual

i) How the eye sees a real object or a real image

It is convenient to imagine that the rays entering the eye are, in effect, 'projected' backwards along straight lines by the eye/brain, and where they appear to cross, a point is seen in focus. Rays are said to be ‘real’ when they actually come from an object or image, as in the above diagram. Real images are those such as are produced by a film projector. Rays from the projector produce images on a screen, and rays from the images on the screen enter the eyes.

ii) How the eye sees a virtual image

Again, the rays entering the eye are, in effect, 'projected' backwards along straight lines by the eye/brain, and where they appear to cross, a point is seen in focus. However, in this case the point seen in focus is behind the mirror. The image is not real (it could not be formed on a screen), and rays do not really come from it. The image is called a virtual image and the rays which appear to come from it are called virtual rays.

Properties of images in plane mirrors

The image in a plane mirror is:

1. As far behind the mirror as the object is in front and the line joining a point on the object to the corresponding point on the image is at right angles to the mirror
2. The same size as the object
3. Virtual (it cannot be formed on a screen)
4. Laterally inverted (left and right are interchanged)
The above properties can all be inferred from the laws of reflection.

Laws of refraction

Anything through which light can pass is called a ‘medium’ – this includes air, glass, water and a vacuum. When light passes from one medium to another it changes direction – we say that it is ‘refracted’.

There are two laws of refraction:
1. The incident ray, the refracted ray and the normal at the point of incidence are all in the same plane – hence, they can be drawn on a flat piece of paper, as in the above diagram
2. At the boundary between any two mediums, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for rays of any particular wavelength (this is called Snell's law)
Refractive index

The absolute refractive index of medium (2) is when medium (1) is a vacuum - we denote this by vn2  or n2 or just by n.

In ‘passing’ from a vacuum to a vacuum there would be no deviation, so i1= i2, so n is exactly 1 for a vacuum. It is also very close to 1 for air:

Light bends towards the normal when it passes into a substance of higher refractive index – such as when it passes from air to water or air to glass, and we say that these are ‘optically denser’ than air.

Example

Find ig if ang = 1.5

Example
Find ia if ang = 1.5.

‘Bending’ of a stick under water

In this case, light from the stick passes from water into air, so the rays bend away from the normal. As previously described, the rays that enter the eye are, in effect, 'projected' back along straight lines by the eye/brain, and where they appear to meet, a point is seen in focus - but this point is above the true point of origin of the rays, as indicated in the diagram. This explains why the stick appears to be bent – and why a pond appears to be shallower than it actually is.

Refractive index relationships

(a) It follows from the previous definition that the refractive index of two mediums, for a ray passing from medium (2) to medium (1), is:

(b) When light enters a new medium it changes speed.

.

(the variable 'v' stands for 'velocity' of light in a medium, while the subscript 'v' stands for ‘vacuum’)

But also,

Example

In a vacuum the speed of light is 3.0*108 ms-1. What is it in water? (nwater =1.33)

Example

What is ig?

Light through a parallel sided block

At the successive boundaries:

Thus, the emerging ray is parallel to the incident ray.

Example

Optical fibres

Total internal reflection is a very useful phenomenon. One important application is in optical fibres. If light enters a very thin glass fibre, its angle of incidence is quite large, larger than the critical angle for glass/air, which is about 420. It undergoes successive total internal reflections, and emerges from the other end.

Thin glass fibres are quite flexible. Individual fibres may be less that 0.01mm in diameter, and many hundreds can be bundled together to make a ‘light pipe’, able to transmit light from one end to the other. These are used by engineers and doctors to inspect difficult to reach locations.

Optical fibres are now also used to transmit information such as TV and telephone messages. They are cheaper and lighter than conventional wires.

A photodiode, which is a diode sensitive to the amount of light falling on it, can be used to detect the pulses of light arriving at the end of an optical fibre, allowing a digital light signal to be converted back into the original transmission.

Example

The following represents an optical fibre made of two glasses of different refractive indices, one forming a core and the other the cladding around it. What is the critical angle for the boundary between the two glasses?

Totally reflecting prisms

Triangular prisms with angles of 900, 450, 450 can be used to turn light through 900 or 1800.

The angles of incidence at A, B and C are 450, which is greater than the critical angle for glass/air of about 420. Thus, total internal reflection occurs at these points. Such prisms are used in binoculars.

A Level Physics - Copyright © A C Haynes 1999 & 2004