Physics - Wave Optics Question with Solution | TestHub

The distance of the $n^{th}$ bright band from the central maximum is given by $x_n=n\frac{\lambda D}{d}$

The distance between the $4^{th}$ and $13^{th}$ bright band is $y=(13-4)\frac{{\lambda }_{1}D}{d}=9\frac{{\lambda }_{1}D}{d}$

The distance between the $6^{th}$ and $16^{th}$ bright band is $y=(16-6)\frac{\lambda D}{d}=10\frac{\lambda D}{d}$

Equating the two expressions for $y$:

$9\frac{{\lambda }_{1}D}{d}=10\frac{\lambda D}{d}$

$9{\lambda }_1=10\lambda$

Substituting ${\lambda }_1=6000$:

$9\times 6000=10\lambda$

$\lambda =\frac{54000}{10}=5400$

Answer: $5400$