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If white light illuminates a diffraction grating having 710 lines/mmlines/mm , over what range of angles does the visible mm

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Complete Question

The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 710 lines/mm, over what range of angles does the visible m = 1 spectrum extend

Answer:

The value
\theta = 16.5 ^ o

Step-by-step explanation:

From the question we are told that

The diffraction grating haves
a =  710 \  lines /mm

Generally the separation of the slit is mathematically represented as


d = (1)/(710) \ mm =0.001408 \ mm =   1.408 *10^(-6) \  m

Generally the condition for constructive interference is mathematically represented as


dsin(\theta ) = n \lambda

So


\theta =  sin ^(-1) [(n * \lambda )/(d) ]

=>
\theta  =  sin^(-1)[(1 *  400 *10^(-9))/( 1.408*10^(-6)) ]

=>
\theta = 16.5 ^ o

User Joseph Quinsey
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