Question

A diffraction grating is illuminated simultaneously with red light of wavelength 660 {\rm nm} and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light.What is the unknown wavelength? (in nm)

Answer 1

Answer:

$\lambda = 420 nm$

Explanation:

As we know that position of maximum on the screen in diffraction pattern is given as

$y = (\frac{2N + 1}{2})\frac{\lambda L}{d}$

here we know that

position of third maximum due to red color light and position of fifth maximum of unknown wavelength are same

so we have

$\frac{7 \lambda_r L}{2d} = \frac{11 \lambda L}{2d}$

so we have

$\lambda = \frac{7}{11} \lambda_r$

$\lambda = \frac{7}{11}(660 nm)$

$\lambda = 420 nm$