Refraction – Snell’s Law

WAVE PROPERTIES Refraction Interactive spreadsheet Refraction is the change in direction at a boundary when a wave travels from one medium to another. Amount of refraction depends on the refractive index of the different media (materials). Normal Air All waves can be Refracted. Refraction is a change of direction due to a change of speed. The example I used involves light rays hitting a glass block. Glass is a medium which is more dense than air. so the light will travel more slowly within the glass block than it would do in air. As the light ray crosses the boundary from one medium to another, it bends. Glass Block Normal 3

Snell’s law Note: medium two is less dense v= speed of wave in the medium

Example 1 A wave travelling at 12 cm s-1 is incident upon a surface at an angle of 55° from the normal. If the angle of refraction is 40°, determine the speed of the wave in the second medium. If the initial wavelength is 6 cm determine the frequency of the wave in the second medium. sinθr = vr sinθi vi sin 40 = vr sin 55 12 vr = 9.4 cm s-1 In first medium: v = fλ f = v/λ = 0.12 / 0.06 = 2.0 Hz Frequency does not change during refraction  f = 2.0 Hz

For light travelling from water into glass, r = 20°. Example 2 For light travelling from water into glass, r = 20°. If nw = 1.33 and ng = 1.50, determine i (θi). video sinθr = ni sinθi nr sin20 = 1.33 sinθi 1.50 sinθi = 0.34 / 0.89 = 0.38 θi = sin-1 0.38 = 22.7°

Total Internal Reflection The Endoscope

You will need… A semicircular block A power pack A ray box A single slit A protractor A ruler A pencil

Total internal reflection Draw on your normal line half way up the block at 90o Shine an incident ray into P You should see a refracted ray P i You should also see a partially reflected ray r The angle of reflection should be equal to the angle of incidence

Gradually increase the angle of incidence. The angle of refraction will increase until the refracted ray emerges along the boundary We call the angle of incidence at this position the critical angle c We label the critical angle, c

The sine of the angle in air = n x the sine of the angle in the block Remember the law of refraction when the light ray is leaving the glass block The sine of the angle in air = n x the sine of the angle in the block

The sine of the angle in air = n x the sine of the angle in the block In this case the angle in the air is 90o The angle in the block is c sin 90o = n x sin c Because sin 90o = 1, the equation becomes: 1 = n x sin c c r How can this equation be rearranged? n = 1 sin c sin c = 1 n or

What is the refractive index for your block?

Calculate the critical angle for glass with a refractive index of 1.59 sin c = 1 n sin c = 1/1.59 sin c = 0.629 c = 39.0o

Total internal reflection If the angle of incidence is increased beyond the critical angle, the light ray is totally internally reflected i r The angle of reflection, r is equal to the angle of incidence, i

Total Internal Reflection allows light to travel around corners Normal i r

The Endoscope

The Endoscope Two bundles of optical fibres next to each other One bundle shines light into the cavity The second bundle of optical fibres has a lens over the end of the fibres allowing an image to be formed using a digital camera

Endoscope laser surgery A laser on the endoscope can carry out surgical procedures It can be used to cauterise blood vessels The colour of the laser can be matched to the tissue to ensure maximum absorption Retinal eye surgery can be carried out by laser by shining a laser through the pupil for a very short time