X-ray spectrum — UPSC Physics Optional CSE 2021 Paper II

An X-ray beam of wavelength \lambda_1 undergoes a first order Bragg reflection at a Bragg angle of 30^\circ. X-ray of wavelength 97\,\mathrm{nm} undergoes 3rd order reflection at a Bragg angle of 60^\circ. Consider that the two beams are reflected from the same set of planes. Find the value of \lambda_1.