Question

In double slit experiment, the angular width of the fringes is $0.20{}^{\circ }$ for the sodium light $(\lambda =5890\mathring{A})$ . In order to increase the angular width of the fringes by 10%, the necessary change in wavelength is

• A. zero
• B. increased by $6479\mathring{A}$
• C. decreased by $589\mathring{A}$
• D. increased by $589\mathring{A}$

Answer 1

Answer: (D)

Let $\lambda$ be wavelength of monochromatic light incident on slit $S$, then angular distance between two consecutive fringes, that is the angular fringe width is
$\theta =\frac{\lambda }{d}\dots$(i)
where, $d$ is distance between coherent sources.

Given, $\frac{\Delta \theta }{\theta }=\frac{10}{100}$
So, from Eq. (i)
$\frac{\Delta \lambda }{\lambda }=\frac{\Delta \theta }{\theta }=\frac{10}{100}=0.1$
$\Rightarrow \Delta \lambda =0.1\lambda$
$=0.1\times 5890\mathring{A}=589\mathring{A}$ (increases)