Question

When illuminated with monochromatic light, a double slit produces a pattern that is a combination of single-slit diffraction and double-slit interference. This can be easily seen if the separation between the slits and the size of slits are related by simple fractions.

Find the ratio of the width of each slit to the separation between the slits, if the first minimum of the single-slit pattern falls on bright fringe number 3 of the double-slit pattern. (This will greatly reduce the intensity of that maximum of the double-slit pattern.)

Answer 1

Let

D – width of each slit

d – separation between slits

For first minimum of the single-slit:

$Dsinθ = λ \\ D = \frac{λ}{sinθ}$

For third double-slit maxima:

$dsinθ = 3λ \\ d = \frac{3λ}{sinθ} \\ \frac{D}{d} = \frac{λ}{sinθ} \times \frac{sinθ}{3λ} = \frac{1}{3}$

Answer: 1/3