Question

White coherent light $(400nm-700nm)$ is sent through the slits of a $YDSE(d=0.5mm,D=50cm)$. There is a hole in the screen at a point $1.0mm$ away (along the width of the fringes) from the central line
(i) Which wavelength will be absent in the light coming from the hole?
(ii) Which wavelength(s) will have a strong intensity?

• A. (i)$400nm$ absent (ii) $\lambda =667nm$
• B. i)$300nm$ absent (ii) $\lambda =687nm$
• C. i)$460nm$ absent (ii) $\lambda =567nm$
• D. i)$420nm$ absent (ii) $\lambda =767nm$

Answer 1

Answer: (A)

(i)$400nm$ absent (ii) $\lambda =667nm$

$\beta =\frac{D\lambda }{d}$
$n\frac{D\lambda }{d}=y$
$(n+\frac{1}{2})\frac{D\lambda }{\lambda }=y$
$\frac{50\times {10}^{-2}}{0.5\times {10}^{-3}}$ $\lambda =1\times {10}^{-3}$
$⟹n^1\lambda (100\times 10)={10}^{-3}$

$⟹n^1\lambda ={10}^{-6}$
$n^1\times (400\leftrightarrow 700)\times {10}^{-9}={10}^{-6}$
$⟹n^{2}x(400\leftrightarrow 700)={10}^3$
$n^1=2.5⟹n=2$
$400nm$ absent
$n=1\frac{3}{2}\lambda =1000$
$\lambda =667nm$