In geometric optics, we only consider light travelling in straight lines.
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:
Laws of reflection
There are two laws of reflection:
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:
REFRACTION AT PLANE SURFACES (return to start of page)
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:
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.
Find ig if ang = 1.5
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
(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’)
In a vacuum the speed of light is 3.0*108 ms-1. What is it in water? (nwater =1.33)
What is ig?
Light through a parallel sided block
At the successive boundaries:
Thus, the emerging ray is parallel to the incident ray.
TOTAL INTERNAL REFLECTION (return to start of page)
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.
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.
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A Level Physics - Copyright © A
C Haynes 1999 & 2004