Question

A light of wavelength $5890$ 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. $4.945\times {10}^{-7}m$
• D. $1.945\times {10}^{-7}m$

Answer 1

The correct option is A $2.945\times {10}^{-7}m$

If thin appears dark
$2=\mu t\cos r=n\lambda$ for normal incident $r=0^o$
$\Rightarrow 2\mu t=n\lambda \Rightarrow t=\frac{n\lambda }{2\mu }$
$\Rightarrow t_{min}=\frac{\lambda }{2\mu }=\frac{5890\times {10}^{-10}}{2\times 1}=2.948\times {10}^{-7}m$