Other Ch. 9 Equations

Question 1

Angle at which first minimum occurs in single-slit diffraction

Answer 1

θ = λ/b

(b = slit width. θ - in radians)

Question 2

Constructive interference for thin film interference (conditions for bright fringe with 1 inversion)

Answer 2

2dn = (m+½)λ

Question 3

Destructive interference for thin film interference (conditions for dark fringe with 1 inversion)

Answer 3

2dn = mλ

Question 4

Angle at which first minimum occurs for diffraction in a circular aperture (minimum angular separation (radians) for 2 points to be just resolved)

Answer 4

θ = 1.22(λ/b) (it’s basically the angle for single slit diffraction but multiplied by a 1.22 constant)

Question 5

Resolvance of a diffraction grating

Answer 5

R = λ/Δλ = mN (Δλ = smallest possible resolvable wavelength difference, m = diffraction order, n = number of slits illuminated)

Question 6

Angles at which constructive interference occurs in a diffraction grating

Answer 6

d sinθ = nλ

θ - angle between a line from the centre of the diffraction grating to central maximum and a line from the centre of the diffraction grating to nth maximum

d = distance between slits

λ = wavelength of light

n = order of maximum (which maximum we’re looking at)

Question 7

Observed frequency (Doppler effect) when a source is moving towards an observer:

Answer 7

f’ = f(v/(v-vs)) (f = emitted frequency, v = velocity of wave, vs = velocity of source)

Question 8

Observed frequency (Doppler effect) when a source is moving away from an observer:

Answer 8

f’ = f(v/(v+vs)) (f = emitted frequency, v = velocity of wave, vs = velocity of source)

Question 9

Observed frequency (Doppler effect) when an observer is moving towards a source:

Answer 9

f’ = f((v+v0)/v) (f = emitted frequency, v = velocity of wave, vo = velocity of observer)

Question 10

Observed frequency (Doppler effect) when an observer is moving away from a source:

Answer 10

f’ = f((v-v0)/v) (f = emitted frequency, v = velocity of wave, vo = velocity of observer)

Question 11

Doppler effect for light

Answer 11

Δf/f = Δλ/λ = approx. v/c (v = relative speed of observer and light)

Question 12

Intensity of a wave

Answer 12

Directly proportional to intensity squared * amplitude squared