Question

In YDSE, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by.

• A. 12
• B. 18
• C. 24
• D. 30

Answer 1

The correct option is B 18

We know fringe width $\beta =\frac{\lambda D}{d}\Rightarrow \beta \propto \lambda$
When wavelength is decreased from 600 nm to 400 nm, the fringe width also decreases by a factor of
$\frac{4}{6}=\frac{2}{3}$
$\Rightarrow$ The number of fringes in the same segment will increase by a factor of $\frac{3}{2}$
The number of fringes observed in the same segment = $12\times \frac{3}{2}=18$