Question

The figure below shows the path of white light’s rays which leave in phase from two small sources $S_1$ and $S_2$ and travel to a point X on a screen. The path difference is $S_{2}X-S_{1}X=8.7\times {10}^{-7}m$. What wavelength of light gives complete destructive interference at X?

• A. $4.0\times {10}^{-7}m$
• B. $4.4\times {10}^{-7}m$
• C. $6.6\times {10}^{-7}m$
• D. $5.8\times {10}^{-7}m$

Answer 1

The correct option is D $5.8\times {10}^{-7}m$

Path diff. = $(2n+1)\frac{\lambda }{2}$ for destructive interference.
$\therefore 8.7\times {10}^{-7}=\frac{(2n+1)\lambda }{2}$
$\lambda =\frac{17.4\times {10}^{-7}}{(2n+1)}=\frac{17400\dot{A}}{(2n+1)}$
$n=0,{\lambda }_1=17400\dot{A}$. Not possible (as this wavelength lies in infrared region).
$n=1,{\lambda }_2=5800\dot{A}$. Possible because this wavelength lies in visible region
$n=2,{\lambda }_3={3480}^{\circ }\dot{A}$. Not possible because this wavelength lies in ultra - violet region.