a diffraction grating is illuminated simultaneously with red light of wavelength 700 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.

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06-12-2022
Physics

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a diffraction grating is illuminated simultaneously with red light of wavelength 700 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.

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ShubhamSrivastavaidn ShubhamSrivastavaidn · Answer 1 · 2022-12-13T00:51:09-05:00

Unknown wavelength λ= 420nm

Given data

Wave length = 700nm

The fifth order overlaps the third order maximum.

DIFFRACTION GRATING?

The problem can be solved using the idea that since fifth-order maximum exactly overlaps the third-order maximum of the red light . Therefore, the value of for the fifth order maxima is equal to that of third order maxima.

mλ=asinθ

Here, a is the slit-width , m is the order and θ is the angular separation ∴λ1 [tex]m_{1}[/tex]=λ2 [tex]m_{2}[/tex]

[tex]700nm(3)=[/tex]λ2(5)

∴λ2 = [tex]\frac{700(3)}{5}[/tex]

λ2 = 420nm

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DIFFRACTION GRATING?

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