Question

In Young's double slit experiment, the wavelength of red light is $7800\mathring{A}$ and that of blue is $5200\mathring{A}.$ The value of $n$ for which $n^{th}$ bright band due to red light coincides with $(n+1{)}^{th}$ bright band due to blue light is-

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Given, ${\lambda }_R=7800\mathring{A};{\lambda }_B=5200\mathring{A}$

$n^{th}\text{bright band due to red light}=(n+1{)}^{th}\text{bright band due to blue light}$

$\frac{n{\lambda }_{R}D}{d}=\frac{(n+1){\lambda }_{B}D}{d}$

$n\left(7800\right)=(n+1)\left(5200\right)$

$\Rightarrow 3n=2(n+1)$

$\Rightarrow n=2$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.