What is the wavelength in nm of a light whose first order bright band forms a diffraction angle of 30 degrees, and the diffraction grating has 700 lines per mm?

714.285 nm

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) is rewritten as:  

(2)  

We know:  

In addition we are told the diffraction grating has 700 lines per mm, this means:  

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

(3)  

(4)  

Knowing :

This is the wavelength of the light

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hope this