In Young's double slit experiment, the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 A 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 a…

Question

In Young's double slit experiment, the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 A 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

Accepted Answer

(2) 1.9 mm. Given: d=2 mm at θ₁=0.20°; wanted, the d that gives θ₂=0.21° at the same λ and D. Idea: the angular width of a fringe is θ=λ/d, so at fixed λ the angle and the separation are inversely related. (θ₁)/(θ₂)=(d₂)/(d₁). d₂=d₁(θ₁)/(θ₂)=2×(0.20)/(0.21). =(0.40)/(0.21). =1.90 mm. The quoted λ and D are consistent with the given 0.20° but are not needed for the ratio.

Step-by-step solution

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