Diffraction

Question 1

what happens to the wavefront of a wave if it passes through a gap

Answer 1

the wavefronts spread out into the ‘shadow’ region

Question 2

what is it called when this happens

Answer 2

diffraction

Question 3

how would the spread of the wavefronts change if the oscillator in a ripple tank had its frequency increased

Answer 3

• the wavelength would shorten

- so the spreading would be reduced

Question 4

what does narrowing the aperture of the gap between two barriers do to the spreading of the wave

Answer 4

it increases it

Question 5

what condition needs to be met in order for the diffraction pattern (wavefronts) to look circular

Answer 5

the width of the gap needs to be similar to the wavelength of the incident wave

Question 6

what did huygen describe the composition of wavefronts as

Answer 6

• he said every point on a wavefront is the source of secondary spherical wavelets
• these spread out with the wave velocity

Question 7

in that case what would the new wavefronts be

Answer 7

the envelope of the secondary wavelets

Question 8

why do the wavefronts then spread out when obstructed by a slit / barrier

Answer 8

• the secondary wavelets at the edges of the barrier are transmitted into a geometrical shadow
• causing the diffraction spreading

Question 9

what is the equation for finding the angle between the central maximum and the first minimum

Answer 9

• sin@ = Y/a
• Y = wavelength
• a = the width of the slit

Question 10

what is the general consensus when it comes to creating a diffraction pattern using a slit (already said)

Answer 10

the wavelength should be the same order of magnitude as the width of the slit

Question 11

what approximation could be used if the angle for sin@ is less than 20 degrees

Answer 11

that sin@ = tan@ = @ radians

Question 12

what are diffraction gratings

Answer 12

• 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

Question 13

what is monochromatic light

Answer 13

light with one specific and constant wavelength (of light)

Question 14

how are the patterns produced from diffraction gratings different than normal patterns

Answer 14

• the maxima occur at specific angles
• where the small coherent waves from each groove or slit superimpose constructively
• producing sharply defined lines

Question 15

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

Answer 15

measure the angle between the central maximum and the diffracted maxima

Question 16

what is the equation for this

Answer 16

• 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)

Question 17

how would you practically draw this up firstly

Answer 17

• 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

Question 18

how would you then calculate the wavelength of the light using the triangle

Answer 18

• 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

Question 19

what are diffraction gratings actually used for in the real world

Answer 19

• determining the wavelengths of unknown sources

- and identifying elements by measuring the wavelenghts of line spectra

Question 20

what is the resolving power of the eye determined to be

Answer 20

• the smallest angular separation of objects

- for which two or more can be distinguished separately

Question 21

why do objects that are very close together seem to be merging according to the human eye

Answer 21

• 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

Question 22

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

Answer 22

• 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

Question 23

what is the mass and charge of an electron

Answer 23

• 9.11x10-31 kg

- 1.6x10-19 C

Question 24

what is the equation to work out the wavelength of an electron

Answer 24

• Y = h/mv
• Y = lambda
• h = plancks constant
• m = mass
• v = velocity

Question 25

what is plancks constant

Answer 25

6.63x10-34 Js

Question 26

how were the wave-like properties of electrons discovered

Answer 26

by diffracting electrons through crystal lattices

Question 27

how is electron diffraction simply done in an a vacuum tube

Answer 27

• 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

Question 28

how are the electrons accelerated through the vacuum tube and why does it work

Answer 28

• 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

Question 29

why can electrons be diffracted through crystal lattices anyway

Answer 29

• 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

Question 30

how does the fluorescent screen work

Answer 30

• 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

Question 31

what does the diffraction pattern look like

Answer 31

• concentric rings

- with a definitive circle in the middle

Question 32

what would be the effect of increasing the voltage on the diffraction pattern and why

Answer 32

• 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