Question

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

Answer 1

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`