Superposition

Question 1

Principle of Superposition

Answer 1

The principle of superposition states that when two or more waves of the same kind meet at a point in space, the resultant displacement at that point is equal to the vector sum of the displacements of the individual waves at that point

Question 2

Standing Wave

Answer 2

A stationary (or standing) wave is the result of interference between two progressive waves of the same type, frequency, amplitude and speed, travelling along the same line but in opposite directions

Question 3

Diffraction

Answer 3

Diffraction is the bending (or spreading) of waves after passing through an aperture or round an obstacle

Question 4

Coherence

Answer 4

Waves or sources are said to be coherent if they have a constant phase difference

Question 5

Interference

Answer 5

Interference is the superposition of two or more coherent waves to give a resultant wave whose resultant amplitude is given by the principle of superposition

Question 6

Constructive Interference

Answer 6

Constructive interference occurs when two waves arrive at the same point with a phase difference of zero

Maximum intensity and amplitude is obtained

Question 7

Destructive Interference

Answer 7

Destructive interference occurs when two waves arrive at the same point with a phase difference of π rad

Minimum intensity and amplitude is obtained

Question 8

Conditions for Observable Interference

Answer 8

The waves or sources must be coherent (i.e. they have the same frequency and a constant phase difference)

The waves must have similar amplitude (for a better contrast)

The waves must overlap and be of the same type (to produce regions of constructive and destructive interference)

For transverse waves, they must be unpolarised or polarised in the same plane

Question 9

Path Difference

Answer 9

Path difference is the difference in the distances that each wave travels from its source to the point where the two waves meet

Question 10

Young’s Double Slit Experiment

Answer 10

x = λD/a, where x = fringe separation, λ = wavelength, D = distance from slit to screen, a = slit separation

Formula is applicable only if a < d and a > λ

Question 11

Diffraction Grating

Answer 11

dsinθn = nλ, where 𝜃n = angular position of nth
order bright fringe from central maxima, n = order of maxima, λ = wavelength

In order to determine maximum order of bright fringes, sinθn < 1 –> nλ/d < 1 –> n < d/λ

Question 12

Single Slit Diffraction

Answer 12

sinθ = nλ/b, where b = width of slit, n = order of minima, λ = wavelength, θ = angular position of nth order dark fringe from central maxima

Question 13

Rayleigh Criterion

Answer 13

θmin ≈ λ/b, where θmin = minimum angular separation of the sources, λ = wavelength, b = width of rectangular slit

Two images are just resolved when the central maximum of one image falls on the first minimum of the other