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?

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 1 year ago

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