Higher Physics – Unit 3

3.2 Refraction of Light

Refraction

θa

θm

θa = angle of incidence in air (larger)

θm = angle of incidence in material

When light passes from air into a material the ratio is constant. m

a

θ sinθ sin

Material Refractive Index n

glass 1.5

perspex 1.47

water 1.33

diamond 2.4

2

1

θ sinθ sin

n

The absolute refractive index, n, of a medium is given by:

where θ1 is the angle in a vacuum (air is used as an approximation) and θ2 is the angle in the medium.

Example

A ray of light shines into a block of perspex. Calculate angle x

200

x

nθ sinθ sin

m

a

1.47x sin

20 sin

1.4720 sin

x sin

13.5x

Worksheet – Radiation & Matter Tutorial

Q18, 19

Outcome 3 Refractive Index of a Perspex

Block

normalθa

θpB

A

C

Place the block on white paper and trace around its outline.

Draw in the normal at the midpoint B.

With incident angle θa = 100, measure the angle θp, the refracted angle in the perspex.

Repeat for other values of incident angle.

Use an appropriate format to determine the refractive index of the perspex block.

Refractive Index

The refractive index can also be found using:

m

a

vv

n

m

a

λλ

n

speed of light in air (3x108 ms-1)

speed of light in material (ms-

1)

wavelength of light in air (m, nm)

wavelength of light in material (m, nm)

Frequency

Light of wavelength 600nm in air is shone through glass of refractive index 1.5.

Calculate: a) speed of light in the glass

b) wavelength of light in the glass

c) frequency of light in the air

d) frequency of light in the glass

2 x 108 ms-1

400nm

5 x 1014 Hz

5 x 1014 Hz

Conclusion

The frequency of a wave is determined by its source and does not change in different media.

fair = fmaterial

Snell’s Law

Refractive index depends on the frequency of the incident light.

Refraction occurs because a wave travels at different speeds in different media.

The refractive index is equal to the ratio of the speeds, giving:

but as frequency is constant this cancels to:

2

1

2

1

2

1

f λf λ

vv

sinθsinθ

n

2

1

2

1

2

1

λλ

vv

sinθsinθ

n

Worksheet – Radiation & Matter Tutorial

Q20, 22, 23, 24

normal

critical angle

small incident anglemaximum incident angle

total internal reflection

large incident angle

Critical Angle

normal

θa

θp

B

C

Critical Angle of a Perspex Block

Make measurements of various incident angles θp and the corresponding refracted angle θa to determine the critical angle θc for the perspex block.

Critical Angle Formula

When the angle in the medium is equal to the critical angle, the angle in air is 900

So applying Snell’s Law: normal

θc

900

m

a

θ sinθ sin

n

cθ sin90 sin

n

cθ sin1

n

But because sin 90 = 1

or

n1

θ sin c

Example

The refractive index of glass is 1.5. Calculate the critical angle.

n1

θ sin c

1.51

θ sin c

.....666.0θ sin c

0c 8.41θ

Worksheet – Radiation & Matter Tutorial

Q25, 26, 27, 28