refraction diffraction and intereference

two conditions for sources to be coherent

• waves must have a constant phase difference

• waves must have same frequency

refractive index

• n=\frac{c}{v}

• refractive index of air is approx. 1

Snell’s law

• n1 sin theta = n2 sin theta

n1\sin\theta1=n2\sin\theta2

total internal reflection

• theta c = n2/n1

fibre optics

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

• communication optical fibre allows pulses to light to enter from an transmitter and reach a receiver at the other end - must be highly transparent - minimise absorption which would otherwise reduce the amplitude of pulses the further they travel

• each fibre consists of a core surrounded by a layer of cladding of a lower refractive index to reduce light loss from core as this would otherwise reduce amplitude as well

• TIR takes place at core - cladding boundary as at each point where this occurs, the angle of incidence of pulse exceed critical angle

• core must be very narrow to prevent modal (multi path) dispersion - occurs in a wide core as light travelling along the axis of the core travels a shorter distance per metre of fibre than light that repeatedly undergoes TIR - pulse would become too long and merge with the next pulse

• material dispersion - pulse dispersion also occurs when white light is used instead of monochromatic light. the speed of light in the glass depends on its wavelength. violet travels slower than red in glass - difference in speed between each wavelength of light would lengthen pulses as one component falls behind

• pulse broadening

path difference

young’s double slit

• light passes through a single narrow slit first which acts as a single source diffracting light to both slits - the path lengths between the single slit and tghe double slit are constant / fixed / the same

• this light then passes through two closely spaced double slits which act as cohernt sources of waves

• alternate dark and bright fringes can be seen on a screen which are caused by the interference of light from the two slits

bright and dark fringes

• diffraction patterns from both slits overlap and interfere

• constructive superposition of waves from two slits - reinforcement at bright fringe - peaks meet peaks and troughs meet troughs

• waves from each slit meet in phase - path difference n lambda