Diffraction Flashcards
what happens to the wavefront of a wave if it passes through a gap
the wavefronts spread out into the ‘shadow’ region
what is it called when this happens
diffraction
how would the spread of the wavefronts change if the oscillator in a ripple tank had its frequency increased
- the wavelength would shorten
- so the spreading would be reduced
what does narrowing the aperture of the gap between two barriers do to the spreading of the wave
it increases it
what condition needs to be met in order for the diffraction pattern (wavefronts) to look circular
the width of the gap needs to be similar to the wavelength of the incident wave
what did huygen describe the composition of wavefronts as
- he said every point on a wavefront is the source of secondary spherical wavelets
- these spread out with the wave velocity
in that case what would the new wavefronts be
the envelope of the secondary wavelets
why do the wavefronts then spread out when obstructed by a slit / barrier
- the secondary wavelets at the edges of the barrier are transmitted into a geometrical shadow
- causing the diffraction spreading
what is the equation for finding the angle between the central maximum and the first minimum
- sin@ = Y/a
- Y = wavelength
- a = the width of the slit
what is the general consensus when it comes to creating a diffraction pattern using a slit (already said)
the wavelength should be the same order of magnitude as the width of the slit
what approximation could be used if the angle for sin@ is less than 20 degrees
that sin@ = tan@ = @ radians
what are diffraction gratings
- patterns on surfaces which have thousands of equally spaced parallel grooves scored onto each centimeter
- or with thousands of equally spaced microscopic gaps
- with the intent of diffracting incoming light
what is monochromatic light
light with one specific and constant wavelength (of light)
how are the patterns produced from diffraction gratings different than normal patterns
- the maxima occur at specific angles
- where the small coherent waves from each groove or slit superimpose constructively
- producing sharply defined lines
if you know the number of lines per meter on the grating, what do you need to do in order to calculate the wavelength of light transmitted by the grating
measure the angle between the central maximum and the diffracted maxima
what is the equation for this
- nY (lambda) = d sin@
- n = number of rays away from the central maximum (order of maximum)
- d = the distance between two lines in the grating (slit separation)
how would you practically draw this up firstly
- you measure the distance between the central maximum and the other diffracting maximum (n = x)
- this could be told to you as the xth order
- measure the distance between the diffraction grating and the sheet the rays are reflecting off of
- the central maximum is used for this (this is l)
- connect the end of the line from the central maximum to the nth maximum to the beginning of the central maximum line to make a triangle
how would you then calculate the wavelength of the light using the triangle
- the angle between l and n=0 to n=x makes a right angle
- so you have a right angled triangle
- @ is the angle formed at the diffraction grating
- meaning the third line drawn is the hypotenuse
- l is the adjacent
- and n=0 to n=x is the opposite
- as you know the length of the opposite and adjacent sides, you use tan work out what the angle is
- tan^-1 = O/A, giving you @
- you then plug this @ into the equation to work out the wavelength
- the n before Y is taken as the nth order
what are diffraction gratings actually used for in the real world
- determining the wavelengths of unknown sources
- and identifying elements by measuring the wavelenghts of line spectra
what is the resolving power of the eye determined to be
- the smallest angular separation of objects
- for which two or more can be distinguished separately
why do objects that are very close together seem to be merging according to the human eye
- because when the light from them passes through the pupil diffraction occurs
- as the images get closer their diffraction patterns begin to overlap on the retina
- when the central maximum of one coincides with the first minimum of the other they can just be resolved as separate entities
- but any more than that and they begin to merge into a single image
using the equation a = Y/D where a is the angle between the light from two objects and D is the diameter of the aperture, why do telescopes have higher resolutions than eyes
- because they have objective lenses with larger diameters
- with D increasing but Y remaining constant, the angle between the objects could decrease before they arent distinguishable
- meaning the angular separation is smaller and therefore has a higher resolution
what is the mass and charge of an electron
- 9.11x10-31 kg
- 1.6x10-19 C
what is the equation to work out the wavelength of an electron
- Y = h/mv
- Y = lambda
- h = plancks constant
- m = mass
- v = velocity
what is plancks constant
6.63x10-34 Js
how were the wave-like properties of electrons discovered
by diffracting electrons through crystal lattices
how is electron diffraction simply done in an a vacuum tube
- high velocity electrons are fired from the electron gun to the graphite crystal
- there is a fluorescent screen on the other side where the electrons diffracting patterns can be observed
how are the electrons accelerated through the vacuum tube and why does it work
- by using high voltages
- E = QV, and as the charge of an electron is constant, a high voltage will give the electron alot of kinetic energy
- as KE = mv^2 / 2 where m is constant, an increase in energy leads to an increase in its speed
why can electrons be diffracted through crystal lattices anyway
- they have a regular hexagonal structure
- with atomic separations similar to the electrons wavelength
- therefore the condition for the width of the slit to be similar to the incident wave is met
how does the fluorescent screen work
- parts of the screen that come into contact with charged particles glow
- so when the negatively charged electrons hit it parts of it will glow
- allowing us to see the diffraction pattern produced
what does the diffraction pattern look like
- concentric rings
- with a definitive circle in the middle
what would be the effect of increasing the voltage on the diffraction pattern and why
- increasing the voltage means the speed of the electrons would increase
- using the Y = h / mv equation, that means the wavelength of the electrons would decrease
- this results in the diffraction (angle) being dramatic
- creating rings that are closer together with smaller diameters on the screen
