Question

The first dark spot from a diffraction pattern made using a laser of wavelength 510 nm is at an angle of 24 degrees from the centerline. Find the width of the slits. What happens to the pattern if the slit width is changed to 200 nm?

Answer 1

Wavelength of light used = $\lambda$ = 510 nm.

Angular position of n = 1 st order dark fringe is $\theta$ = 24^o with respect to the centerline.

So, the slit width d is given by : d sin $\theta$ = n$\lambda$

or, d = n$\lambda$ / sin $\theta$ = 1 x 510 nm / sin 24^o ~ 1254 nm.

So, slit width is 1254 nm.

Since, slit width d is directly proportional to sin $\theta$ , reducing slit width to 200 nm will reduce sin $\theta$ , and hence $\theta$ , that means, the fringes will become closer.