When monochromatic light is being used with a certain diffraction grating, it is found that the first-order maximum occurs at 8°. What is the highest order of maximum that can be observed?Diffraction

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valentin68 eNotes educator| Certified Educator

For a diffraction grating, having incident light at an angle `theta_i` to the diffraction grating, the angle `theta_k` of observed `k`  order maxima satisfy the following

`d*[sin(theta_i) +sin(theta_k)] =k*lambda`     (1)

where `d` is the distance between two consecutive scratches on the grating. For normal incident light `theta_i =90 degree` and first order maxima `k=1` one has

`d*sin(theta_1) =lambda` or `lambda/d =sin(theta_1)`

The highest value of `k` is obtained for `theta_k =90 degree` when (1) becomes

`d =k*lambda`

`k =d/lambda =1/sin(theta_1) =1/sin(8) =7.18 =7`

The highest order of maxima that can be observed is 7

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