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
$\theta=\frac{\lambda}{d} \ldots$(i)
where, $d$ is distance between coherent sources.

Given, $\quad \frac{\Delta \theta}{\theta}=\frac{10}{100}$
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)