Question: 10: In a Young’s double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm , then the number of fringes he would observe in the same region of the screen is
(1) 9
(2) 12
(3) 6
(4) 8
Answer: Option (2)
Explanation:
In Young’s double slit experiment, the fringe width is given by
\beta = \frac{\lambda D}{d},
where \lambda is the wavelength of light, D is the distance between the slit and the screen, and d is the separation between the slits.
The number of fringes observed in a given fixed length on the screen is inversely proportional to the fringe width.
Hence, the number of fringes N is inversely proportional to the wavelength:
N \propto \frac{1}{\lambda}.
Let N_1 = 8 be the number of fringes corresponding to wavelength
\lambda_1 = 600 \text{ nm}, and
N_2 be the number of fringes for wavelength \lambda_2 = 400 \text{ nm}.
Using the proportionality,
\frac{N_2}{N_1} = \frac{\lambda_1}{\lambda_2}.
Substituting the values,
\frac{N_2}{8} = \frac{600}{400} = \frac{3}{2}.
N_2 = 8 \times \frac{3}{2} = 12.
Therefore, the number of fringes observed with wavelength 400 nm is 12.