Question

In a Young's double slit experiment, $16$ fringes are observed in a certain segment of the screen when light of wavelength $700 nm$ is used. If the wavelength of light is changed to $400 nm$, 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.
$\rightarrow$ We can write
$N w =\ell$
$N \left(\frac{\lambda D }{ d }\right)=\ell$
$\frac{ N _{1} \lambda_{1} D }{ d }=\ell$
$\frac{ N _{2} \lambda_{2} D }{ d }=\ell$
$N _{1} \lambda_{1}= N _{2} \lambda_{2}$
$16 \times 700= N _{2} \times 400$
$N _{2}=28$