Physics Question on single slit diffraction

Question

Angular width of the central maxima in the Fraunhofer diffraction for $\lambda$ = 6000 � is $\theta_{0}$ . When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is,

Answer 1

Solution

Angular width $\propto \frac{\lambda}{d}$
$\Rightarrow \frac{\theta_{0}}{0.7\theta_{0}} = \frac{\frac{6000\,�}{d}}{\frac{\lambda}{d}}$
$\Rightarrow \lambda = 4200 \,�$