A diffraction grating has rulings of 890 lines/mm. When white light is incident normally on the grating, what is the longest wavelength that forms an intensity maximum in the fifth order

225nm

Explanation:

The Maxima of diffraction girating

dsin( θ)= m(λ)

Where θ)= angle between central axis and corresponding point

The wavelength is to corresponding sin( θ)

Then the maximum number of (λ) can be seen by setting sin( θ)= 1 then

d= m(λ)

At fifth order maximum m=1 then

d= 5(λ)

Where d= distance between the slit and with girating of 1/890rullig/mm

d= 1/890rullig/mm= 8.90×10^-6m

At maximum wavelength

d= 5(λ)

(λ)=5/d

= 8.90×10^-6m/5

=2.75*10^-7

= 275nm

Therefore, longest wavelength that forms an intensity maximum in the fifth order is 275nm

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