North Berwick High School

Department of Physics

Higher Physics

Unit 2 Particles and Section 6 of

Section 6 Refraction of Light

Note Making Make a dictionary with the meanings of any new words.

Waves 1. Copy the definitions of , period and energy. Include the example on page 2.

Wave characteristics 1. Copy the sentence on characteristics.

Reflection 1. Copy the formula and diagram on page 3.

Refraction 1. Explain how light is refracted through a medium. State the effect on frequency.

Refractive index 1. Describe an experiment to measure the refractive index of a medium. 2. Write a note on refractive indices, including the formula and the example given.

Refractive index and frequency of light 1. Show how white light can be split into its component colours. You need to know these in order of .

Refractive index and relationship with v,  and  1. Copy the formula and example on page 7

Critical angle and total internal 1. Describe an experiment to measure the critical angle of a medium. 2. State what happens when the angle in the medium is greater than the critical angle. Fibre- 1. Copy the note on fibre-optics.

Relationship between critical angle and refractive index 1. Copy the note on the relationship between critical angle and refractive index and include both examples.

Section 6 Refraction of Light

Contents

Content Statements ...... 1

Waves ...... 2

Frequency of a wave...... 2

Period of a wave ...... 2

Energy of a wave ...... 3

Wave characteristics ...... 3

Reflection ...... 3

Refraction ...... 4

Refraction of light ...... 4

Refractive index ...... 4

Refractive index and frequency of light ...... 6

Refractive index and relationship with v,  and  ...... 7

Critical angle and total internal reflection ...... 8

Fibre-optics ...... 8

Relationship between critical angle and refractive index ...... 9

Problems ...... 11

Solutions ...... 15

Content Statements

Content Notes Context a) Refraction. Refractive index of a material Optical instruments using . as the ratio of the sine of angle of incidence in of high power (air) to the sine of angle of beams due to hot centre with refraction in the material. lower refractive index. Refractive index of air Design of lenses, dispersion of treated as the same as that signals in optical fibres, colours of a vacuum. seen in cut . Investigations should include situations where light travels from a more dense to a less dense substance. Refractive index as the ratio of in vacuum (air) to the speed in the material. Also as the ratio of the . Variation of refractive index with frequency. b) Critical angle Investigating total internal Semicircular blocks. and total reflection, including critical Reflective road signs, internal angle and its relationship reflectors (, periscopes, reflection. with refractive index. SLR cameras). Optical fibres for communications, medicine and sensors.

1

Section 6 Refraction of Light

Waves

Frequency of a wave

The frequency of a wave (f) is the number of complete waves (N) which pass a point in one second. Frequency is measured in hertz (Hz). The frequency of a wave is the same as the frequency of the source producing it.

f = N t

Period of a wave

The period of a wave (T) is the time taken for one complete wave to pass a point, or the time taken to produce one complete wave. Period is measured in seconds (s). It is the inverse of the frequency.

T = 1 f

Example

Find the period of a wave with a frequency of 40 Hz.

1 1 Period T =  = 0.025 s. f 40

2

Energy of a wave

The energy of a wave depends on its amplitude; the larger the amplitude, the more energy it has. The amplitude of curved waves, such as ripples produced when a pebble is dropped into water, decreases as they spread out, since the total energy of the wave is spread out over a larger .

Wave characteristics

All waves exhibit reflection, refraction, and interference.

Reflection

Angle of incidence = angle of reflection

 i =  r

normal

Speed, frequency and wavelength all stay the same.

3

Refraction

When waves travel from one medium to another, they are refracted. This happens because the speed of the wave changes on entering the new medium. If the waves enter the medium at an angle to the normal, then their direction also changes. The greater the change in speed, the greater the change in direction.

A decrease in speed means the direction moves towards the normal, and vice versa.

The frequency of the wave never changes and is determined by the source. It can only be altered at source.

Refraction of light

Refractive index

By varying the angle a, a relationship between a and g can be found.

sin Experiment shows that a is constant. sin g

This constant is called the reflective index, n, of the medium.

sin Ɵa sin a = n sin g

sin Ɵg 4

The values given in data books are called absolute refractive indices. These are the ratios of the sine of the angle in a vacuum, not air, to the sine of the angle in the medium. However, for most practical purposes we can use air.

sina = n a = angle in air measured relative to normal sinm

m = angle in medium measured relative to normal.

The refractive index measures the effect a medium has on light. The greater the refractive index, the greater the change in speed and direction.

The refractive index of a medium is the same whether light moves from air into the medium or vice versa.

The absolute refractive index is always a value greater than (or equal to) 1 and has no units.

Example

Using information from the diagram, find the refractive index of the clear . All angles must be measured from the normal.

° ° a = 90 – 30 = 60 m = 90 – 54 = 36

° m =36 sin sin 60 n = a = = 1.47 sinm sin 36

5

Refractive index and frequency of light

The refractive index of a medium depends upon the frequency (colour) of the incident light.

When light enters a prism, it separates into its component colours and produces a spectrum. This happens because each colour (frequency) is refracted by a different amount.

Since violet is refracted more than red (i.e. it has changed speed and direction by a greater amount), it follows that the refractive index for violet light must be greater than the refractive index for red light.

nviolet > nred

6

Refractive index and relationship with v,  and 

The refractive index can also be calculate from the change in velocities or the change in wavelengths.

sin v  n = a = a = a sinm vm m

In general, from medium 1 to medium 2:

sin v  1 = 1 = 1 sin2 v2 2

Example

Calculate the speed of light in glass of refractive index 1.50.

8 va va 3  10 8 -1 = n = 1.50 = 1.50 vm = 2 × 10 m s vm vm vm

7

Critical angle and total internal reflection

When light travels from a medium of high refractive index to one of lower refractive index (e.g. glass into air), it bends away from the normal. If the angle within the medium m is increased, a point is reached where the angle in a becomes 90°.

The angle in the medium which causes this is called the critical angle, c.

If the angle in the medium is greater than the critical angle, then no light is refracted and Total Internal Reflection takes place within the medium.

m < c m = c m >c

Fibre-optics

A thin glass fibre uses the principle of total internal reflection. The rays of light always strike the internal surface of the glass at an angle greater than the critical angle.

A commercial optical fibre has a fibre of high refractive index surrounded by a thin, outer cladding of glass with lower refractive index than the core. This ensures that total internal reflection takes place.

8

Relationship between critical angle and refractive index

At the critical angle, m = c and a = 90

sin sin 90 1 a = = sin sin sin m c c

1 n = sinc

Total internal reflection is more likely to take place in a material with a small critical angle; therefore, it is desirable to use a medium of high refractive index when designing optical fibres.

Examples

1. Calculate the critical angle for water of refractive index = 1.33.

1 1 sin  = = 0.752 c n 1.33

c = 49

9

2. A of light strikes the inside of a glass block as shown. Will the ray emerge from the glass?

1 1 sinc  = n 1.5

c = 41.8

The angle inside the glass is 60, which is greater than 41.8.

Hence total internal reflection occurs.

10

Refraction of light Problems

Refraction of light

1. A ray of monochromatic light passes from air into rectangular blocks of different materials A, B and C as shown.

Calculate the refractive index n of each of the materials for this light.

2. A ray of monochromatic light passes from air into a thin glass walled container of water, a rectangular block of and a rectangular block of as shown in the diagrams.

Calculate the values of the angles x, y and z in each of the diagrams.

11

3. A ray of monochromatic light passes from air into a certain material as shown.

The refractive index of the material is 1·35.

a) Calculate the value of angle r. b) Calculate the velocity of the light in the material.

4. A ray of light of wavelength 6·00 × 107 m passes from air into glass as shown.

a) Calculate the refractive index of the glass for this light. b) Calculate the speed of this light in the glass. c) Calculate the wavelength of this light in the glass. d) Calculate the frequency of this light in air. e) State the frequency of this light in the glass.

12

5. A ray of light of wavelength 500 nm passes from air into perspex.

The refractive index of the perspex for this light is 1·50.

a) Calculate the value of angle r. b) Calculate the speed of light in the perspex. c) Calculate the wavelength of this light in the perspex.

6. The refractive index for red light in is 1·513 and for violet light it is 1·532.

(a) Using this information, explain why white light can produce a spectrum when passed through crown glass.

(b) A ray of white light passes through a semi-circular block of crown glass as shown and produces a spectrum.

i. Which exit ray is red and which exit ray is violet? ii. Calculate the angle of refraction in air for each of the exit rays. iii. Find angle x, the angle between the red and violet rays.

13

7. A ray of white light is dispersed, by a glass prism, producing a spectrum S.

The angle x is found to be 0·7. The refractive index for red light in this glass is 1·51.

Calculate the refractive index for blue light.

14

Solutions

Refraction of light

1. material A n = 1·27 material B n = 1·37 material C n = 1·53

2. (a) x = 32·1° (b) y = 40·9 ° (c) z = 55·9°

3. (a) 21·7 ° (b) 2·2 × 108 m s 1

4. (a) 1·52 (b) 1·97 × 108 m s 1 (c) 3·95 × 107 m (d) 5·0 × 1014 H (e) 5·0 × 1014 Hz

5. (a) 30·7° (b) 2.00 × 108 m s1 (c) 3.33 × 107 m

6. (b) (ii) ray 1 = 60·20°, ray 2 = 61·49º (iii) 1·29°

7. 1·54

15