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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)

Respuesta :

Answer:

[tex]\lambda = 420 nm[/tex]

Explanation:

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

[tex]y = (\frac{2N + 1}{2})\frac{\lambda L}{d}[/tex]

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

[tex]\frac{7 \lambda_r L}{2d} = \frac{11 \lambda L}{2d}[/tex]

so we have

[tex]\lambda = \frac{7}{11} \lambda_r[/tex]

[tex]\lambda = \frac{7}{11}(660 nm)[/tex]

[tex]\lambda = 420 nm[/tex]

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