Angular width of central maximum in the Fraunhoffer's diffraction pattern is measured. Slit is illuminated by the light of another wavelength, angular width decreases by 30%. Wavelength of light used is

4200 Å

For first diffraction min. $d \sin θ =λ$

and if angle is small, $\sin θ = θ$

$dθ =λ$

i.e. Half angular width, $θ =\frac{λ}{d}$

Full angular width w = $2θ =\frac{2λ}{d}$

Also $w' = \frac{2λ'}{d}$

$∴\frac{λ'}{λ}=\frac{w'}{w}$ or $λ'=λ\frac{w'}{w}$

$= 6000 × 0.7 = 4200Å$