devarshi-dt-logo

Question:

In Young's double slit experiment, the slits are separated by 0.5mm and the screen is placed 1.0m away from the slit. It is found that the 5th bright fringes are at a distance of 4.13 mm from the 2nd dark fringe. Find the wavelength of light used.

Solution:

Given that
d=0.5mm=5×10⁻³m
D=1m
5th bright form 2nd dark
y5th bright=(7/2 ×λD/d)=4.13 mm = fringe width
β=(λD/d) ⇒7β/2 ×λD/d=4.13×10⁻³
2×λD/2d=4.13×10⁻³
λD/d=4.13×10⁻³
λ×1/(5×10⁻³)=4.13×10⁻³
λ=4.13×5×10⁻³×10⁻³
λ=20.65×10⁻⁶m
λ=20650×10⁻¹⁰m
λ=20650Å
Thus, wavelength of light used=λ=5900Å