Question

White light is used to illuminate the two slits in Young's double-slit experiment. The separation between two slits is $x$ and the screen is at distance $z>>x$ from the slits. At a point on the screen directly in front of one of the slit which wavelength is absent?

• A. $\frac{2 x^{2}}{z}$
• B. $\frac{3 x^{2}}{z}$
• C. $\frac{x^{2}}{5 z}$
• D. $\frac{x^{2}}{2 z}$

Answer 1

Answer: (C)

$y_{n^{t h}} \, dark=\frac{\left(2 n - 1\right) \lambda D}{2 d}$ $=\frac{\left(2 n - 1\right) \times z}{2 x}$
$\frac{x}{2}=\frac{\left(2 n - 1\right)}{2}\frac{\lambda z}{x}$
$\lambda =\frac{x^{2}}{\left(2 n - 1\right) z}$
$\lambda =\frac{x^{2}}{z}$ for $n=1$
$\lambda =\frac{x^{2}}{3 z}$ for $n=2$
$\lambda =\frac{x^{2}}{5 z}$ for $n=3$