Question

A light of wavelength $5890 \,\mathring{A}$ falls normally on a thin air film. The minimum thickness of the film such that the film appears dark in reflected light is

• A. $2.945 \times 10^{-7} m$
• B. $3.945 \times 10^{-7} m$
• C. $4.95 \times 10^{-7} m$
• D. $1.945 \times 10^{-7} m$

Answer 1

Answer: (A)

If thin film appears dark
$2 \mu t\, \cos r=n \lambda$ for normal incidence $r=0^{\circ}$
$\Rightarrow 2 \mu t=n \lambda \Rightarrow t=\frac{n \lambda}{2 \mu}$
$\Rightarrow t_{\min }=\frac{\lambda}{2 \mu}=\frac{5890 \times 10^{-10}}{2 \times 1}$
$=2.945 \times 10^{-7} m$