Question

In a Young's double slit experiment the wavelength of red light is $7.8\times {10}^{-5}$ cm and that of blue light is $5.2\times {10}^{-5}$. The value of n for which (n + band coincides with nth bright red band is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$\frac{yd}{D}=\left(n-1\right){\lambda }_r$

$\frac{yd}{D}=n{\lambda }_r$

$\Rightarrow \frac{5.2\times {10}^{-5}}{7.8\times {10}^{-5}}=\frac{n-1}{n}$

$\Rightarrow \frac{2}{3}=1-\frac{1}{n}$

$\Rightarrow \frac{1}{n}=\frac{1}{3}$

$\Rightarrow n=3$

Hence,

option $\left(C\right)$ is correct answer.