Question

If the distance between the first maxima and fifth minima of a double-slit pattern is $7mm$ and the slits are separated by $0.15mm$ with the screen $50cm$ from slits, then wavelength of the length used is

• A. $600nm$
• B. $525nm$
• C. $467nm$
• D. $420nm$

Answer 1

The correct option is A $600nm$

Path difference between first maxima and fifth minima, $7\times {10}^{-3}=\frac{(2\times 5-1)\lambda D}{2d}-\frac{\left(1\right)\lambda D}{d}=\frac{7\lambda D}{2d}$

$\lambda =\frac{7\times {10}^{-3}\times 2d}{7D}=\frac{7\times {10}^{-3}\times 2\times 15\times {10}^{-5}}{7\times 50\times {10}^{-2}}=0.6\times {10}^{-6}m=600nm$