When illuminated with monochromatic light, a double slit produces a pattern that

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 arc 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 2 of the double-slit pattern. (This will greatly reduce the intensity of that maximum of the double-slit pattern.)

Explanation / Answer

let D is the width of each slit and d is the distance between the slits.

lamda is the wavelength of the light and R is the distance between slit and screen.

In single slit first minimum, y1_single = lamda*R/D

in double slit second maximum, y2_double = 2*lamda*R/d

given

y2_double = y1_single

2*lamda*R/d = lamda*R/D

==> D/d = 1/2

= 0.5

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