Question

White light reflected at normal incidence from a soap film has minima at $6500\stackrel{\circ }{A}$ and maxima at $7500\stackrel{\circ }{A}$ in the visible region with not minima in between. If $\mu$ is $\frac{5}{3}$ for the thin film, the thickness of film is :

• A. $7.40\times {10}^{-7}cm$
• B. $9.75\times {10}^{-5}mm$
• C. $9.70\times {10}^{-7}cm$
• D. $9.75\times {10}^{-4}mm$

Answer 1

The correct option is A $7.40\times {10}^{-7}cm$

For minima to occur,
$2\mu t=2n\frac{{\lambda }_1}{2}.....\left(i\right)$
and for maxima
$2\mu t=(2n-1)\frac{{\lambda }_2}{2}....\left(ii\right)$
From Eqs. (i) and (ii), we get
$(2n-1){\lambda }_2=2n{\lambda }_1$
or $(2n-1)7500=\left(2n\right)6500$
[given, ${\lambda }_2=7500\stackrel{\circ }{A},{\lambda }_1=6500\stackrel{\circ }{A}]$
or $1500n-7500=13000n$
or $2000n=7500$
or $n=3.75$
Substituting the value of $\left(n\right)$ in Eq. (i), we get
$2\times \frac{5}{3}\times t=2\times 3.75\times \frac{6500}{2}\times {10}^{-10}[\because \mu =\frac{5}{3}]$
$\Rightarrow t=7.40\times {10}^{-7}cm$.