Refraction Of Light - High School Physics Form 3

Refractive index can be given in terms of velocity by the use of the following equation;
n2 = velocity of light in medium 1/velocity of light in medium 2
When a ray of light is travelling from vacuum to a medium the refractive index is referred to as absolute refractive index of the medium denoted by 'n'
Refractive index of a material 'n' = velocity of light in a vacuum/velocity of light in material 'n'
The absolute refractive indices of some common materials is given

Material	Refractive Index
Air (ATP)	1.00028
Ice	1.31
Water	1.33
Ethanol	1.36
Kerosene	1.44
Glycerol	1.47
Perspex	1.49
Glass (crown)	1.55
Glass (flint)	1.65
Ruby	1.76
Diamond	2.72

Example 3
A ray of light is incident on a water-glass interface as shown. Calculate 'r'. (Take the refractive index of glass and water as 3/2 and 4/3 respectively)

Solution

Since anw sin θw = ang sing
4/3 sin 300 = 3/2 sin r
3/2 sin r = 4/3 × 0.5
Sin r = 4/6 × 2/3 = 4/9 = 0.4444
r = 26.40

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Example 4
The refractive index of water is 4/3 and that of glass is 3/2. Calculate the refractive index of glass with respect to water.
Solution

wng = gna × ang, but wna = 1/anw = 3/4
wng = 3/4 × 3/2 = 9/8 = 1.13

Real and apparent depth
Consider the following diagram

- The depth of the water OM is the real depth, and the distance IM is known as the apparent depth.
- OI is the distance through which the coin has been displaced and is known as the vertical displacement.
- The relationship between refractive index and the apparent depth is given by;
Refractive index of a material = real depth/apparent depth


Example 5
A glass block of thickness 12 cm is placed on a mark drawn on a plain paper. The mark is viewed normally through the glass. Calculate the apparent depth of the mark and hence the vertical displacement. (Refractive index of glass =3/2)
Solution

ang = real depth/apparent depth
apparent depth = real depth/ang = (12 × 2)/3 = 8 cm
vertical displacement= 12 - 8 = 4 cm

Applications Of Refractive Index
Total internal reflection
- This occurs when light travels from a denser optical medium to a less dense medium.
- The refracted ray moves away from the normal until a critical angle is reached usually 900 where the refracted ray is parallel to the boundary between the two media.
- If this critical angle is exceeded total internal reflection occurs and at this point no refraction occurs but the ray is reflected internally within the denser medium.

Relationship Between The Critical Angle And Refractive Index

Consider the following diagram

From Snell’s law
gnw = sin C/sin 900,but ang = 1/gna since sin 900 = 1
Therefore ang= 1/sin C, hence sin C=1/n or n=1/sin C

Example 6
Calculate the critical angle of diamond given that its refractive index is 2.42
Solution

Sin C = 1/n = 1/ 2.42 = 0.4132 = 24.40

Effects Of Total Internal Reflection
1. Mirage: These are ‘pools of water’ seen on a tarmac road during a hot day. They are also observed in very cold regions but the light curves in opposite direction such that a polar bear seems to be upside down in the sky.
2. Atmospheric refraction: the earths’ atmosphere refracts light rays so that the sun can be seen even when it has set. Similarly the sun is seen before it actually rises.

Applications Of Total Internal Reflection

1. Periscope: a prism periscope consists of two right angled glass prisms of angles 450,900 and 450 arranged as shown below.
They are used to observe distant objects.

2. Prism binoculars: the arrangement of lenses and prisms is as shown below. Binoculars reduce the distance of objects such that they seem to be nearer.

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3. Pentaprism: used in cameras to change the inverted images formed into erect and actual image in front of the photographer.

4. Optical fibre: this is a flexible glass rod of small diameter. A light entering through them undergoes repeated internal reflections. They are used in medicine to observe or view.

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5. Dispersion of white light: the splitting of light into its constituent colours is known as dispersion. Each colour represents a different wavelength as they strike the prism and therefore refracted differently as shown.

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