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

`\lambda = 420 nm`

Step-by-step explanation:

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

`y = ((2N + 1)/(2))(\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

`(7 \lambda_r L)/(2d) = (11 \lambda L)/(2d)`

so we have

`\lambda = (7)/(11) \lambda_r`

`\lambda = (7)/(11)(660 nm)`

`\lambda = 420 nm`