A diffraction grating is illuminated simultaneously with red light of wavelength 670 nm and light of an unknown wavelength. The fifth-order (m=5) maximum of the unknown wavelength exactly overlaps the third-order (m=3) maximum of red light.

What is the unknown wavelength?

402 nm .

Explanation:

Let the wave length of unknown light be λ .

For fifth order maxima the condition is

path difference at the point of fringe = 5 λ

For red light of 670 nm , for 3 rd order maxima

path difference at the point of fringe = 3  x wave length

= 3 x 670 nm

From these two equations

5 λ = 3 x 670 nm

λ = 3 x 670 / 5 nm

= 402 nm .

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