Question

A diffraction pattern is produced on a viewing screen by using a single slit with blue light. Does the pattern broaden or contract (become narrower) (a) when the blue light is replaced by red light (b) when the slit width is increased?

Answer 1

(a) Expands

(b) decreases

Solution:

As per the question:

Width of the central maxima for a single slit diffraction can be given as:

`w = (2\lambda d)/(x)`

where

w = width

`\lambda = wavelength`

x = slit width

Now,

From the above expression, width, w is proportional to the wavelength and slit width is in inverse proportion to the width of the central maxima.

w ∝
`\lambda`

And

w ∝
`(1)/(x)` (1)

We know that, red light has the longest wavelength whereas blue light has the shortest wavelength:

`\lambda_(red)` >
`\lambda_(red)`

width of the central maxima is greater for red light than for blue light

(a) Thus on replacing by red light the pattern broaden

(b) From eqn (1):

When the slit width, x is increased the width of the central maxima, w decreases.