Two parallel beams of monochromatic light pass through a long slit of width 0.2 mm one by one. The angular divergence in which most of the light is diffracted for both the beams are $2.25 × 10^{-3}\, rad$ and $4.50 × 10^{-3}\, rad$ respectively. If the wavelength of the first beam is 3000 Å, then the wavelength of the second beam is:

6000 Å

The correct answer is Option (3) → 6000 Å

Given slit width same, single-slit first minima angle approx: $ \theta \approx \frac{\lambda}{a} $ so $ \frac{\lambda_2}{\lambda_1}=\frac{\theta_2}{\theta_1} $

$\lambda_1=3000\,\text{\AA}=3.0\times10^{-7}\,\text{m}$

$\lambda_2=\lambda_1\frac{\theta_2}{\theta_1} =3.0\times10^{-7}\times\frac{4.50\times10^{-3}}{2.25\times10^{-3}} =3.0\times10^{-7}\times2 =6.0\times10^{-7}\,\text{m}$

Converting to angstroms: $6.0\times10^{-7}\,\text{m}=6000\,\text{\AA}$

Answer: $6000\,\text{\AA}$