Question

In Young's experiment, the wavelength of red light is $7.8\times {10}^{-5}cm$ and that of blue light is $5.2\times {10}^{-5}cm.$ The value of ${\left(n\right)}^{th}$ for which ${\left(n+1\right)}^{th}$ blue bright band coincides with $\left(n\right)$ red band is

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is C 2

$x\underset{Blue}{{}_{\left(n+1\right)}}=\left(\frac{\left(n+1\right)D}{d}\right)$
$=\left[\frac{\left(n+1\right)D{\lambda }_B}{\alpha }\right]$
$x_n\underset{\mathrm{Re}d}{{}^{}}=\frac{nD{\lambda }_{\mathrm{Re}d}}{d}$
$x_{\underset{Blue}{\left(n+1\right)}}=x_n\underset{\mathrm{Re}d}{{}^{}}\Rightarrow \frac{\left(n+1\right)D{\lambda }_B}{d}=\frac{nD{\lambda }_{\mathrm{Re}d}}{d}$
$\left(\frac{\left(n+1\right)}{n}\right)=\left(\frac{{\lambda }_{\mathrm{Re}d}}{{\lambda }_B}\right)=\frac{7.8\times {10}^{-5}}{5.2\times {10}^{-2}}$
$\Rightarrow 2n+2=3n\Rightarrow n=2$