Question

A single slit of width $a$ is illuminated by violet light of wavelength $400\text{nm}$. The width of the central maximum is measured as $y$. When half of the slit width is covered and illuminated by yellow light of wavelength $600\text{nm}$, the width of the central maximum is,

• A. zero and the patten vanishes
• B. $\frac{y}{3}$
• C. $3y$
• D. none of these

Answer 1

The correct option is C $3y$

In single slit experiment width of central maximum, $y=2\beta =\frac{2\lambda D}{a}$
$\Rightarrow y\propto \frac{\lambda }{a}$
$\Rightarrow \frac{y^{\prime }}{y}=\frac{{\lambda }^{\prime }}{\lambda }\times \frac{a}{a^{\prime }}=\frac{600}{400}\times \frac{a}{\left(\frac{a}{2}\right)}$
$\therefore y^{\prime }=3y$

Hence, $\left(C\right)$ is the correct answer.