Question

A diffraction grating has 300 lines per mm. If light of wavelength 630 nm is sent through this grating, what is the highest order maximum that will appear?

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Answer 1

Concepts and reason

The concepts that are used to solve this problem are diffraction of light through the grating and trigonometry identity.

Initially, write the expression of diffraction of light due to the grating in terms of wavelength and width of grating and then use the condition for maximum order of diffraction.

Finally, calculate the maximum order of diffraction for the given wavelength of light.

Fundamentals

Write the general expression of diffraction of light through the grating.

Here, is the wavelength of the light wave, is the angle between the diffracted ray and the grating’s normal vector, is the integer that represents the order of maxima, is the grating separation or the distance between slits.

The general expression of diffraction of light through the grating is,

Rearrange for the .

For the maximum value of , the value of should be maximum. Hence, the maximum value of is .

Substitute, for .

The maximum order of diffraction for the given wavelength of light is calculated by using the expression of diffraction of the light due to the grating.

Provided that a diffraction grading has . It means that the grating separation or the distance between slits, is calculated as,

Substitute, for , and for the .

The value of is in fraction. But the order of diffraction should be in integer form. Since, the maximum of the sine function is . Hence, the value of cannot exceed beyond . Therefore, the highest order maximum of diffraction, will be .

Ans:

The highest order maximum is .