37. Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000Å is $θ_0$. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is :

37. Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000Å is $θ_0$. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is :

(a) 420Å

(b) 1800Å

(c) 4200Å

(d) 6000Å

Answer :  (c) 4200Å

\(\theta_w = \frac{2\lambda}{a}\)

\(\theta_w = \frac{2 (6000 \mathring{A})}{a}\)

\(0.7 \theta_w = \frac{2 \lambda_2}{a}\)

\(\lambda_2 = 0.7 (6000 \mathring{A})\)

\(= 4200 \mathring{A}\)