Light emitted by element X passes through a diffraction grating that has 1200 slits/mm/mm. The interference pattern is observed on a screen 79.0 cmcm behind the grating. First-order maxima are observed at distances of 58.2 cmcm , 65.2 cmcm , and 92.5 cmcm from the central maximum. What are the wavelengths of light emitted by element X?

The wavelengths are

Explanation:

From the question we are told that

The number of slits per mm is N = 1200

The distance of the screen is

The first distance where First-order maxima is observed is

The second distance where First-order maxima is observed is

The second distance where First-order maxima is observed is

Generally the distance of separation between the slits is mathematically represented as

Considering the first distance where First-order maxima is observed

Generally the the first distance where First-order maxima is observed is mathematically represented as

=>

=>    

=>    

Considering the second distance where First-order maxima is observed

Generally the the second distance where First-order maxima is observed is mathematically represented as

=>

=>    

=>    

Considering the third distance where First-order maxima is observed

Generally the the third distance where First-order maxima is observed is mathematically represented as

=>

=>    

=>    

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