Refraction, refractive index and dispersion by a prism

What refraction is

A coin at the bottom of a tumbler of water looks raised, closer to the surface than it is. This happens because light bends as it leaves the water. The bending of light when it passes obliquely (at a slant) from one medium into another is refraction. Light travels at different speeds in different media. Going from a rarer medium such as air into a denser one such as glass, it slows down and bends towards the normal. Going from denser to rarer, it speeds up and bends away from the normal. A ray that falls along the normal goes straight through without bending. The frequency of light does not change in refraction; only its speed and wavelength change. Colour depends on frequency, so a red bulb still looks red when seen from under water.

Refractive index and the two laws of refraction

• The refractive index (n) of a medium tells how much it bends light. n = c/v: the speed of light in vacuum divided by its speed in the medium.
• c = 3 × 10⁸ m/s. Refractive index is a ratio of two speeds, so it has no unit.
• A higher n means light is slower in that medium and bends more. Water is about 1.33 and glass about 1.5.
• First law: the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
• Second law (Snell's law): the ratio sin i / sin r is a constant, equal to the refractive index for that pair of media.
• Here i is the angle of incidence and r is the angle of refraction, both measured from the normal.

Activity and how to draw: refraction through a glass slab

You need a drawing board, a white sheet, a rectangular glass slab, four pins, a protractor and a scale.

1. 1
   Fix the white sheet on the board. Place the slab in the middle and draw its outline ABCD with a sharp pencil. AB is the face the light will enter.
2. 2
   Draw a straight line slanting towards face AB, meeting it at point O. Fix two pins, P and Q, upright on this line, a few cm apart.
3. 3
   Look at P and Q through the opposite face CD. Fix two more pins, R and S, so that they appear in one straight line with the images of P and Q.
4. 4
   Remove the slab and the pins. Join the marks of R and S and extend the line to meet CD at O′. Join O and O′.
5. 5
   Draw normals (dotted lines at 90° to the faces) at O and O′. Label the incident ray PQO, the refracted ray OO′ and the emergent ray O′RS.
6. 6
   Measure ∠i at O, between the incident ray and the normal. Measure ∠r, between OO′ and the same normal. Measure ∠e at O′, between the emergent ray and the normal there. Extend the incident ray beyond O as a dotted line to show the lateral displacement (the sideways gap between it and the emergent ray).
7. 7
   Observe: ∠r is smaller than ∠i, so the ray bent towards the normal inside the glass. ∠e = ∠i, so the emergent ray is parallel to the incident ray but shifted sideways.

   The bending at the two parallel faces is equal and opposite.

Refractive index from speed and from angles

Dispersion of white light by a prism

• A prism is a block of glass whose faces for light to enter and leave are flat but not parallel, such as a triangular prism.
• When a narrow beam of white light (sunlight) passes through a prism, it splits into a band of seven colours. This band is a spectrum.
• The splitting of white light into its colours is dispersion.
• Cause: the refractive index of glass is different for each colour, so each colour bends through a different angle.
• Violet bends the most and red the least. The order is VIBGYOR: violet, indigo, blue, green, yellow, orange, red.
• A rainbow is a natural spectrum. Raindrops in the air disperse sunlight, like tiny prisms.

Activity: make a spectrum with a prism and sunlight

1. 1
   Take an empty cardboard box. Cut a rectangular window in one side and cover it with thin white tracing paper. This is your screen.
2. 2
   On the opposite side, cut a thin vertical slit with a knife.
3. 3
   Place a glass prism on a small block inside the box, between the slit and the screen.
4. 4
   Turn the slit towards sunlight, and turn the prism slowly until colours fall on the paper.
5. 5
   Observe the coloured band on the tracing paper and note the order of the colours.

   Red is bent least and violet most. Never look straight at the Sun.
6. 6
   To draw it, make a triangle for the prism and one ray marked white light going in. Draw a widening fan coming out, with red at the top and violet at the bottom.