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?
The distance between maxima stays the same.T
he distance between maxima increases.
The distance between maxima decreases.
Not enough information given.
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.