Question

In a double-slit experiment, light with a wavelength λ passes through a double-slit and forms an interference pattern on the screen at a distance L from the slits. What statement is true for the resulting interference pattern if the frequency of the light increases?

OPTIONS:

The distance between maxima stays the same.T

he distance between maxima increases.

The distance between maxima decreases.

Not enough information given.

Answer 1

Fringe width, (b)is the distance between two consecutive maximas or minima.

The expression for the fringe width is given by;

b = kL/d .............eqn 1

where k= wavelength of the light used

L= distance of the screen from the slits

d = seperation between the slits.

Also, wavelength (k) and frequency (v) are related by the expression

c= vk .........eqn 2

where c is the velocity of light

or we can rearrange the equation 2 as

k = c/v .........eqn 3

Eqn 3 indicats that k is inversely proportional to v. i.e wavelength of light is inversely prportional to the frequency.

i.e More the frequency, lesser would be the wavelength and vice versa.

Using value of k from eqn 3 in eqn 1 , we get

b = cL/vd

this equation clearly states that fringe width b is also inversely proportional to frequency v of the light.

Hence, if we increase the frequency, fringe width would decrease i.e distance between two consecutive maxima would decrease.