Optics

Refraction

Explaining refraction

• Occurs because speed of light is different in each substance

• Amount of refraction depends on the speed

• Equation: sini/sinr = c / c(s) where c(s) is the speed of light in the substance

• Therefore n = c / c(s) where n is the refractive index

• So the smaller the speed of light in a substance the greater the refractive index

• As frequency doesn’t change n = λ / λ(s)

Refraction at a boundary between two transparent substances

• n1sinθ = n2sinθ

• Assume refractive index of air is 1

• Can use a prism to split a beam of white light into colours of spectrum – happens as light composed of continuous range of wavelengths

• As different wavelengths, each colour refracted by a different amount

• Red least refracted violet most refracted

Total internal reflection

Only takes place if:

• The incident substance has a larger refractive index
• The angle of incidence exceeds the critical angle

Investigating total internal reflection

• If angle of incidence is increased to a certain value known as critical angle, light ray refracts along the boundary

• If angle increased any further the light ray undergoes total internal reflection at boundary

• At critical angle, angle of refraction is 90 so n1sini = n2sin90

• As sin90 is 1, sinθ = n1 / n2 at the critical angle

Optical fibres

• Used in medical endoscopes to see inside the body, and in communications to carry light signals

• Light ray totally internally reflected every time it hits the fibre boundary

• Fibres need to be highly transparent to minimise absorption of light

• Each fibre consists of core surrounded by layer of cladding of lower refractive index than core to reduce light loss

• Total internal reflection takes place at core-cladding boundary – reduces crossover which keeps signals secure

• Core must be very narrow to prevent modal dispersion – occurs in wide core as light repeatedly undergoes total internal reflection – the pulse becomes too long, and could merge with the next pulse

Pulse dispersion

• Pulse dispersion also occurs if white light used instead of monochromatic light

• This material dispersion is due to different wavelengths travelling at different speeds which causes pulses to become longer

• Modal dispersion caused by different angles of entry so narrowing the core means fewer possible angles of entry

Double slit interference

Young's double slit experiment

• Illuminate two closely spaced parallel slits using suitable light source

• Slits act as coherent sources of waves – emit waves with constant phase difference and same freq

• Alternate bright and dark fringes (Young’s fringes) can be seen on a white screen placed where the diffracted light from the double slits overlap

• Fringes are evenly spaced and parallel to double slits

• If single slit is too wide, each part of it produces a fringe pattern which displaced slightly due to adjacent parts of the slit

• As a result dark patches become narrower than light patches and contrast lost

Young's fringes

• Fringes formed due to interference of light from the two slits

• Where bright fringe is formed the light from one slit reinforces the light from the other slit (light is in phase – 2π radians) / λ difference

• Where a dark fringe formed light from one slit out of phase with other slit (cancels out) – phase difference π radians / half a λ difference

• Distance from centre of bright fringe to centre of next is called fringe separation

• This depends on the slit spacing s and the distance D from the slits to the screen

• Equation: Fringe separation w = (λ × D) / s

Interference (more)

Coherence

• Coherent sources emit light of same freq and constant phase difference

• Observed in Young’s double slit experiment

• Light from two nearby lamps cannot form an interference pattern as two light sources emit waves at random – points of cancellation and reinforcement would change at random

Wavelength and colour

• In double slit experiment fringe separation depends on the colour of light used

• Fringe separation greater for red light than blue light

• Due to red light having longer wavelength than blue light so bigger λ means bigger w when looking at equation

Light sources

• Vapour lamps and discharge tubes produce light with dominant colour eg. sodium vapour lamp emits yellow glow due to λ of 590nm (basically monochromatic light source)

• Light from filament lamp or sun consists of continuous spectrum so covers 350 – 650nm

• Laser light is monochromatic – λ dependent on type of laser

• As laser beam almost perfectly parallel and monochromatic, convex lens can be used to focus it to a fine point

• Laser beams convenient source of coherent light

White light fringes

• Central fringe white as every colour contributes at the centre

• Inner fringes blue and red on outside as red fringes more spaced due to longer λ

• Outer fringes merge into indistinct background of white light - becomes fainter with increasing distance as where fringes merge colours reinforce so overlap

Diffraction

Observing diffraction

• Diffraction of waves through a water gap can be observed using a ripple tank

• Diffracted waves spread out more if gap is narrower or λ made larger

• Diffraction of light by a single slit can be demonstrated by directing a parallel beam of light at the slit

• Diffracted light pattern forms central maxima (fringe) with subsidiary maxima’s (fringes) which are half the width of the central fringe

• Peak intensity of each fringe decreases with distance from the centre

• Outer fringes much less intense than the single fringe

Single slit diffraction

• Using different sources of monochromatic light shows that the greater the λ the wider the fringes

• Narrower slit = wider fringes

• W (width of central fringe) = ( λ × 2D) / a where D is the distance between the slit and the screen, and a is the width of the single slit