Physics - Wave Optics Question with Solution | TestHub

The angular width of central maxima is given by $$2\theta =\frac{2\lambda }{\mathrm{a}}$$ where, $\lambda$ = wavelength of light used $\mathrm{a}=$ width of the slit For ${\lambda }_1=6000\mathring{A},2\theta ={\theta }_0$ (given) For another light of wavelength ${\lambda }_2$ (says), the angular wid th decreases by $30\%$ so, $$2\theta =\left(\frac{100-30}{100}\right){\theta }_0=\frac{70}{100}{\theta }_0=0.7{\theta }_0$$ As slit width is constant, so using Eq. (i) for these values, we get $$\begin{array}{c}\frac{{\theta }_0}{0.7{\theta }_0}=\frac{{\lambda }_1}{{\lambda }_2}\\ \Rightarrow {\lambda }_2={\lambda }_1\times 0.7=6000\times 0.7=4200\mathring{A}\end{array}$$