Double Slit Experiment

Question

Two slits are separated by 0.30 mm, but with a finite slit width of 0.075 mm. How many bright fringes will be observed if the wavelength of the laser is 500 nm?

Answer 1

Because each slit has a finite width, single-slit diffraction effects must be taken into consideration.

Step I. Ignore the slit width, find the highest possible number of maxima on each side. d sinθ = m λ becomes d = m λ because the maximum possible value of sinθ is 1. Plug in the numbers, m_max = 600.

Step II. Take into account single-slit diffraction effects. a sinθ = m^' λ is the condition for minima. If you put these two equations together, you find the ratio m/m^' = 0.30/0.075 = 4. This means that every fourth bright spot from double-slit interference overlaps with a dark spot from single-slit diffraction.

Step III. Put everything together. There should be 600 bright spots on each side, but 600/4 = 150 are actually dark. You are left with 600 - 150 = 450 bright fringes on each side.

Step IV. Final answer: the total number of bright fringes is 450 x 2 + 1 = 901 (the factor of 2 is because you take into account the fringes on both sides, +1 because you include the central maximum.