Question

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

Answer 1

We know that: $\theta =\frac{\lambda }{d}$

Given: $\theta ={0.20}^{\circ },\lambda =5896\stackrel{\circ }{A}$

for small fractional change
$\frac{\Delta \theta }{\theta }=\frac{\Delta \lambda }{\lambda }-\frac{\Delta d}{d}$

For constant $d$
$\frac{\Delta d}{d}=0,\frac{\Delta \theta }{\theta }=10\%$ or $\frac{10}{100}$

$\frac{\Delta \theta }{\theta }=\frac{\Delta \lambda }{\lambda }\Rightarrow \Delta \lambda =\frac{\Delta \theta }{\theta }\times \lambda$

$\Rightarrow \Delta \lambda =\frac{10}{100}\times 5890\stackrel{\circ }{A}=589\stackrel{\circ }{A}$

FINAL ANSWER $=589\stackrel{\circ }{A}$