Physics - Wave Optics Question with Solution | TestHub

The angular width of fringes in a double slit experiment is given by $\theta =\frac{\lambda }{d}$

For a constant slit separation $d$, the angular width is directly proportional to the wavelength, so $\theta \propto \lambda$

Taking the fractional change on both sides, we get:

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

Given that the angular width is increased by $10\%$, the wavelength must also increase by $10\%$.

$\Delta \lambda =\frac{10}{100}\times \lambda$

$\Delta \lambda =0.10\times 5890\text{A˚}=589\text{A˚}$

Thus, the necessary change in wavelength is an increase by $589\text{A˚}$.

Answer: increase by $589\text{A˚}$