In Young's double slit experiment the separtion d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to
(1) 1.8 mm (2) 1.7 mm (3) 2.1 mm (4) 1.9 mm
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Angular Width=lambda/d
So, 0.20°= lambda/2mm
So lambda=0.20°×2
lambda/d=0.21°(given)
Now substituting value of lambda,
d=(0.20°×2mm)/0.21°= 1.9mm
So D)
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The separation between the slits needs to be changed to 1.9mm
Separation between the slits = d = 2mm (Given)
Wavelength of the light = 5896Å (Given)
Distance between the screen and slit = 100cm (Given)
Angular width = λ/d
Thus,
0.20° = λ/2
λ = 0.20° × 2
0.21° = λ/d
Substituting the value of λ
d = 0.20° × 2 / 0.21°
d = 1.9
Thus, the separation needs to be changed to 1.9mm
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