Physics - Wave Optics Question with Solution | TestHub

The angular separation of the central maximum in a Fraunhofer diffraction pattern is given by $2\theta =\frac{2\lambda }{a}$, where $a$ is the slit width.

This shows that the angular separation is directly proportional to the wavelength of light used, i.e., $2\theta \propto \lambda$.

Given that the angular separation decreases by $20\%$, the new angular separation becomes $80\%$ of the initial value.

Therefore, the new wavelength ${\lambda }_2$ is $80\%$ of the initial wavelength ${\lambda }_1$.

${\lambda }_2=0.80{\lambda }_1$

${\lambda }_2=0.80\times 6000\text{ A˚}=4800\text{ A˚}$

Answer: $4800\mathring{A}$