(a) Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young’s double slit experiment.
(b) In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.
Answers
The two characteristic difference between interference and diffraction are as follows:
1)Interference is a process where two waves of similar frequency but with a different phase mix with each other .Their are two types of interference ,it can either be destructive interference or it can be constructive interference.
2)Diffraction on the other hand is the phenomenon in which light spreads out while passing through a small opening .
3)In order for diffraction to take place the area through which light will pass should be comparable in size to the wavelength of the light .
4)Diffraction leads to interference because when light spreads out while passing through a point then each point on wavefront acts as an individual source of light and this leads to a path difference.
5)Diffraction and interference go hand in hand but are two different processes.
The formula for the intensity at a point in Young's double slit can be derived followingly
Let y1 and y2
be displacement of two waves having same amplitude a and phase difference \phiϕ between them.
y1 =asinωt
y2 =asin(ωt+ϕ)
Resultant displacement is: y=y1+y2=asinωt+asin(ωt+ϕ)=asinωt(1+cosϕ)+cosωt(asinϕ)
Rcosθ=a(1+cosϕ)
Rsinθ=asinϕ
y=Rsin(ωt+θ)
Where, RR is resultant amplitude at a particular point, I is intensity, squaring the equations we get
(1+cosϕ)=4a^2.
T his is the intensity ant any given point due to interference from a double slit