Question

White light may be considered to be a mixture of waves with $\lambda$ ranging between $3900$ $\stackrel{o}{A}$ and $7800$ $\stackrel{o}{A}$. An oil film thickness $10,000$ $\stackrel{o}{A}$ is examined normally by the reflected light. If $\mu =1.4$, then the film appears bright for.

• A. $4308$ $\stackrel{o}{A}$, $5091$ $\stackrel{o}{A}$, $6222\stackrel{o}{A}$
• B. $4000$ $\stackrel{o}{A}$, $5091$ $\stackrel{o}{A}$, $5600$ $\stackrel{o}{A}$
• C. $4667$ $\stackrel{o}{A}$, $6222$ $\stackrel{o}{A}$, $7000$ $\stackrel{o}{A}$
• D. $4000$ $\stackrel{o}{A}$, $4667$ $\stackrel{o}{A}$, $5600$ $\stackrel{o}{A}$

Answer 1

The correct option is A $4308$ $\stackrel{o}{A}$, $5091$ $\stackrel{o}{A}$, $6222\stackrel{o}{A}$

The film appears bright when the path difference
$\left(2\mu t\cos r\right)$ is equal to odd multiple of $\frac{\lambda }{2}$
i.e $2\mu t\cos r=(2n-1)\lambda /2$ where $n=1,2,3....$
$\therefore \lambda =\frac{4\mu t\cos r}{(2n-1)}$
$=\frac{4\times 1.4\times 10,000\times {10}^{-10}\times \cos 0}{(2n-1)}=\frac{56000}{(2n-1)}\mathring{A}$
$\therefore \lambda =56000\mathring{A},18666\mathring{A},8000\mathring{A},6222\mathring{A},5091\mathring{A},4308\mathring{A},3733\mathring{A}$.
The wavelength which are not within specified range are to be refracted.