Question

A diffraction grating is illuminated simultaneously with red light of wavelength 660 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?

Answer 1

Answer:

$396$ nm

Explanation:

As we know that

$dsin\theta = m\lambda$

Given

Fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light

Therefore , $m\lambda$ value for fifth order maximum of red light will be equal to the third order maximum of red light

For fifth order maximum of red light

$m\lambda = 5 * \lambda$

For fifth order maximum of red light

$m\lambda = 3 * 660$

$3 * 660 = 5 *\lambda\\\lambda = \frac{3*660}{5} \\\lambda = 396$nm