Question

A parallel beam of white light is incident on a thin film of air of uniform thickness. Wavelengths $7200\mathring{A}$ and $5400\mathring{A}$ are observed to be missing from the spectrum of reflected light viewed normally. The other wavelength in the visible region missing in the reflected spectrum is

• A. $6000\mathring{A}$
• B. $4320\mathring{A}$
• C. $5500\mathring{A}$
• D. $6500\mathring{A}$

Answer 1

The correct option is B $4320\mathring{A}$

The wavelength missing from the reflected spectrum must satisfy the condition

$2\mu t=n\lambda$

Where t is thickness of air film

When two wavelengths ${\lambda }_1$ & ${\lambda }_2$ are missing

$2\mu t=n{\lambda }_1=(n+1){\lambda }_2$

or $n\times 7200=(n+1)5400$

$n=3$

The next missing wavelength must satisfy the condition

$n{\lambda }_1=(n+2){\lambda }_2$

$7200\times 3=(3+2){\lambda }_2$

$7200\times 3=5{\lambda }_2$

$\therefore {\lambda }_2=4320A°$