light from a discharge tube containing a particular gas illuminates a diffraction grating and is observed...

light from a discharge tube containing a particular gas illuminates a diffraction grating and is observed on a screen 75.0cm behind the grating. The emission at wavelength 621nm creates a first-order bright fringe 38.0 cm from the central maximum. What is the wavelength of the bright fringe that is 47.3cm from the central maximum?

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Expert Solution

For diffraction grating, we have

where is the diffraction angle for respective wavelength

let ₁ be known wavelength of spectral line so that ₁ = 621 nm and its diffraction angle ₁ is tan^-1 (38/75) = 27^o

Diffraction angle ₂ of unknown wavelength ₂ is given as, ₂ = tan^-1(47.3/75) = 32^o

Hence unknown wavelength ₂ is calculated as,

₂ = [ ₁ / sin ₁ ] sin₂ = [ 621 / sin27 ] sin32 = 725 nm

genius_generous answered 10 months ago

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