Question

A single slit of width $a$ is illuminated by violet light of wave length $400nm$ and width of the diffraction pattern is measured as $y$. Half of the slit is covered and illuminated with $600nm$. The width of the diffraction pattern will be

• A. $\frac{y}{3}$
• B. pattern vanishes and width is zero
• C. $3y$
• D. none of these

Answer 1

Answer: (C)

$3y$

We have width of the diffraction pattern
$\beta =\frac{2\lambda D}{d}$
Let us consider $\beta$ as $y$, then we have
$y=\frac{2\lambda D}{d}$
In the first instance $\lambda =400nm$
$⟹y=\frac{2400D}{d}nm$
In the second instance $\lambda =600nm$ and $d=\frac{d}{2}$
$⟹y^{\prime }=\frac{2600D}{\frac{d}{2}}nm$
Hence$\frac{y}{y^{\prime }}=\frac{1}{3}$
$⟹y^{\prime }=3y$