a) Two slits each of width .05 mm and separated by 0.5 mm in y-direction are ill

Question

a) Two slits each of width .05 mm and separated by 0.5 mm in y-direction are illuminated by laser light travelling in x-direction. The distance between successive interference fringes on a screen 2.0 m away from the plane of the slits in x-direction is measured to be 2.5 mm along y-axis? Calculate the wavelength of the laser light. b) How far from the center of the pattern will the first minimum of the single slit diffraction appear on the screen? c) What will be the number of interference fringes inside the central diffraction peak?

Explanation / Answer

Given
distance to screen, D= 2m
distance between slits, d = 0.5mm
distance between successive fringes, s=2.5mm


a) the distance between 2 successive fringes,
can be formulated as s= (D/d)

so, = sd/D
putting the given values, = 6.25x10^-7m =625 nm (Answer)

b) for single slit diffraction first minima,
angle = /d
if y= distance of first minima from center of pattern
then , y= Dtan = D tan(/d)
solving for y by using given values and values derived in sol a),
we get y= 0.25mm (answer)

c) no of fringe depend on ratio of distance between slits to slit width , n= d/a =0.5/0.05 = 10
this means there are 10 interference maxima on right of the central diffraction peak and 10 on left,
giving total interference fringes= 21 (answer)

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