Question

34.) 5. We perform a multi-slit experiment, using N = 6 slits. The wavelength of the light is lambda = 500nm and the distance of the screen from the slits is D = 15m.

a. Determine the distance of the slits, if the 3rd and 4th order diffraction fringes are 15mm away from each other.

b. How many major fringes are visible on the diffraction pattern if the coherence length of the light is δ= 2 micrometers?

c. How many minor fringes are between between each pair of major ones?

Answer 1

For multiple slits , we have ,

d sin = n ............................(1)

where d is distance between slits , is the angular position of maximum intensity , n is order of maximum and

is wavelength of light

for 3rd order and 4th order maximum, if the respective angular position of maximum are 3 and 4 ,

then we have ,

d sin3 = 3 ...................(2)

d sin4 = 4 ....................(3)

By subtracting eqn.(2) from eqn.(3), we get

d { sin4 - sin3 } =    ..................(4)

if the angles are small , sin tan = y/D

where y is position of maximum on screen and D is distance between screen and slit

Hence eqn.(4) will become , (d/D) { y4 - y3 } =

hence distance d between slits , is given by

d = ( D ) / { y4 - y3 } = ( 500 10-9 15 ) / ( 15 10-3 ) = 500 10-6 m = 0.5 mm

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For N slits , number of minor fringes are N-2 .

Since we have 6 slits , number of minor fringes (6-2) = 4