Question

If yellow light emitted by the sodium lamp in Young’s double-slit experiment is replaced by the monochromatic blue light of the same intensity keeping other parameters constant the new fringe width will:
(A) remain unchanged
(B) increase
(C) decrease
(D) can’t be predicted

Answer 1

The fringe width can be determined by using the formula of the fringe width in Young’s double slit. By using the distance between the screen and slit and the wavelength of the light used, the fringe width can be determined.

Formula used:
The fringe width of the Young’s double slit experiment is given by,
$\beta = \dfrac{{D\lambda }}{d}$
Where $\beta$ is the fringe width, $D$ is the distance of the screen from the slits, $\lambda$ is the wavelength of the light used, and $d$ is the distance between the slits.

Complete step by step answer:
By Young’s modulus experiment,
The fringe width of Young’s double-slit experiment is given by,
$\beta = \dfrac{{D\lambda }}{d}\,..................\left( 1 \right)$
From equation (1), it is very clear that the fringe width and the wavelength of the light used is directly proportional to each other. If the wavelength of the light used is increased, then the fringe width is also increased. If the wavelength of the light decreases, then the fringe width is also decreased.
By comparing the wavelength of the red light with the blue light,
Wavelength of the red light, ${\lambda _R} = 620\,nm$ to $750\,nm$
Wavelength of the blue light, ${\lambda _B} = 450\,nm$ to $495\,nm$
So, the red light is having a greater wavelength than the blue light.
If the red light is replaced by the blue light, then the wavelength is decreased.
By, Young’s modulus equation, If the wavelength decreases then the fringe width also decreases.

Hence, the option (c) is the correct answer.

Note:
From Young’s modulus equation, the fringe width is directly proportional to the wavelength of the light used and the distance between the screen and slit, and it is inversely proportional to the distance between the two slits. As the distance between the slits increases, the fringe width decreases.