Optics Problems - Numerical 22

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22.

Red light of l = 650 nm from a distant source falls on a slit of 0.5 mm width. What is the distance between the two dark bands on each side of the central bright band of diffraction pattern observed on screen placed 1.8 m from the slit?

Suggested solution:

Figure shows the set up. O is the central bright fringe. D₁ and D₂ are the first dark fringe on either side of central maxima. Obviously

Given

= 6.5 x 10^-7m: D = 1.8m, d = 5 x 10m

The distance between D₁ and D^l₁ = 2x = 4.68mm