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  4. A parallel beam of sodium light of wavelength 5890 mathringA is incident on a thin glass plate of refractive index 1.5 such that the angle of refraction in the plate is 60°. The smallest thickness of the plate which will make it dark by reflection

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

Wave Optics

Solution:

The condition for minimum thickness corresponding to a dark band is,
$2\mu t\, cos\,r = \lambda$
$\therefore t = \frac{\lambda}{2\mu \,cos r} $
$= \frac{5890 \times 10^{-10}}{2\times 1.5\times cos \,60^{\circ}} $
$ = 3926 \times 10^{-10} m $
$= 3926 \,\mathring{A}$