Question

From a medium of index of refraction n₁, monochromatic light of wavelength l is incident normally on a thin film of uniform thickness L (where L > 0.1 l) and index of refraction n₂. The light transmitted by the film travels into a medium with refractive index n₃. The value of minimum film thickness when maximum light is transmitted if (n₁< n₂< n₃) is –

• A. $\frac{n_{1}\lambda}{2n_{2}}$
• B. $\frac{n_{1}\lambda}{4n_{2}}$
• C. $\frac{\lambda}{4n_{2}}$
• D. $\frac{\lambda}{2n_{2}}$

Answer 1

Answer: (B)

$\frac{n_{1}\lambda}{4n_{2}}$

Answer 2

Equation of path difference for maxima in transmission (or weak reflection) ;

DP_opt = 2n₂L = $\frac{\lambda_{vaccum}}{2}$, $\frac{3\lambda_{vaccum}}{2}$ ………

̃ 2 $\left\lbrack \frac{n_{2}}{n_{1}} \right\rbrack$ L = $\frac{\lambda}{2}$, $\frac{3\lambda}{2}$, …….. ̃ L = $\frac{\lambda}{4n_{2}}$

(notice that l = wavelength is medium is related to l_vacuum as, l_vacuum = n₁l)