Question

Light from a mercury arc lamp is passed through a filter that blocks everything except for one spectrum line in the green region of the spectrum.
It then falls on two slits separated by 0.6 mm. In the resulting interference pattern on a screen 2.5 mm away, adjacent bright fringes are separated by 2.27 nm. The wavelength is:

• A. $54.48nm$
• B. $0.5448nm$
• C. $544.8mm$
• D. $544.8cm$

Answer 1

The correct option is B $0.5448nm$

$\beta =2.27nm$
$D=2.5mm$
$d=0.6mm$
we know that
$\beta =\frac{D\lambda }{d}$
$\lambda =\frac{\beta d}{D}$
$=\frac{2.27\times {10}^{-9}\times 0.6\times {10}^{-3}}{2.5\times {10}^{-3}}$
$=0.5448\times {10}^{-9}m$
$=0.5448nm$