Question

A parallel beam of sodium light of wavelength 5890 $\stackrel{0}{A}$ is incident on a thin glass plate of refractive index 1.5 such that the angle of refraction in the plate is ${60}^o$. The smallest thickness of the plate which will make it dark by reflection:

• A. 3926 $\stackrel{0}{A}$
• B. 4353 $\stackrel{0}{A}$
• C. 1396 $\stackrel{0}{A}$
• D. 1921 $\stackrel{0}{A}$

Answer 1

The correct option is A 3926 $\stackrel{0}{A}$

Let the thickness of the Glass slab is $t$

The condition for minimum thickness corresponding to a dark band is $2\mu tcosr=\lambda$

$\therefore t=\frac{\lambda }{2\mu cosr}=\frac{5890\times {10}^{-10}}{2\times 1.5\times cos{60}^o}$

$t=3926\times {10}^{-10}m=3926\stackrel{o}{A}$