Physics - Wave Optics Question with Solution | TestHub

For minima to occur,

$2\mu t=2n\frac{{\lambda }_1}{2}$...(i)

and for maxima

$2\mu t=\left(2n-1\right)\frac{{\lambda }_2}{2}$...(ii)

From Equations. (i) and (ii), we get

$\left(2n-1\right){\lambda }_2=2n{\lambda }_1$

or$\left(2n-1\right)7500=\left(2n\right)6500$

$\left[\mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n},\mathrm{ }{\lambda }_2=7500 \stackrel{\circ }{\mathrm{A}}, {\lambda }_1=6500 \stackrel{\circ }{\mathrm{A}}\right]$

or$15000n-7500=13000n$

or$2000n=7500$

or$n=3.75$

Substituting the value of$n$in equation (i), we get

$2\times \frac{5}{3}\times t=2\times 3.75\times \frac{6500}{2}\times {10}^{-10}\left[\because \mu =\frac{5}{3}\right]$

$\Rightarrow t=7.40\times {10}^{-7} \mathrm{m}$