# In a Young's double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength

Question:

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

1. 28

2. 24

3. 18

4. 30

Correct Option:

Solution:

Let the length of segment is " $\ell^{\prime \prime}$

Let $\mathrm{N}$ is the no. of fringes in " $\ell^{\prime \prime}$

and $\mathrm{w}$ is fringe width.

$\rightarrow$ We can write

$\mathrm{N} w=\ell$

$\mathrm{N}\left(\frac{\lambda \mathrm{D}}{\mathrm{d}}\right)=\ell$

$\frac{\mathrm{N}_{1} \lambda_{1} \mathrm{D}}{\mathrm{d}}=\ell$

$\frac{\mathrm{N}_{2} \lambda_{2} \mathrm{D}}{\mathrm{d}}=\ell$

$\mathrm{N}_{1} \lambda_{1}=\mathrm{N}_{2} \lambda_{2}$

$16 \times 700=\mathrm{N}_{2} \times 400$

$\mathrm{~N}_{2}=28$