White light is spread out into its spectral components by a diffraction grating. if the grating has 2000 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum? (assume that the light is incident normally on the grating.)

Explanation:

The diffraction angles when we have a slit divided into parts are obtained by the following equation:  

(1)  

Where:  

is the width of the slit  

is the wavelength of the light  

is an integer different from zero

Now, the first-order diffraction angle is given when , hence equation (1) becomes:  

(2)  

We are told the diffraction grating has 2000lines per cm, this means:  

In addition we know

Solving (2) with the known values we will find :  

(3)  

(4)  This is the angle at which red light appears in first-order spectrum.

Explanation:

It is given that,

If the grating has 2000 lines per centimeter.

Wavelength,

The principal maxima is given by :

Since, d = 1/N and n = 1

So,

So, the angle is 7.35 degrees. Hence, this is the required solution.                                      

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