Question

In a Young's double slit experiment, $16$ fringes are observed in a certain segment of the screen when light of wavelength $700nm$ is used. If the wavelength of light is changed to $400nm$, the number of fringes observed in the same segment of the screen would be :

• A. 28
• B. 24
• C. 18
• D. 30

Answer 1

Answer: (A)

Let the length of segment is " ${\ell }^{\prime \prime }$
Let $N$ is the no. of fringes in " ${\ell }^{\prime \prime }$
and $w$ is fringe width.
$\to$ We can write
$Nw=\ell$
$N\left(\frac{\lambda D}{d}\right)=\ell$
$\frac{N_1{\lambda }_{1}D}{d}=\ell$
$\frac{N_2{\lambda }_{2}D}{d}=\ell$
$N_1{\lambda }_1=N_2{\lambda }_2$
$16\times 700=N_2\times 400$
$N_2=28$