If white light illuminates a diffraction grating having 790 lines/mm , over what range of angles does the visible m = 1 spectrum extend?

We are given the property of the illuminating light:

790 lines/mm

Which is also equivalent to:

790,000 lines/m

Taking the reciprocal of this value will give us the distance per line:

d = 1 m / 790,000 lines

d = 1.2658 * 10^-6 m 

Now we can solve for the range of angles using the formula
λ = d * sin θ 

sin θ  = λ / d

where λ is the wavelength of light and θ is the angle

Now we know that visible light ranges from 400 to 700 nm, therefore we use these values to find the range.

when λ = 400 nm = 400 * 10^-9 m

sin θ = 400 * 10^-9 m / 1.2658 * 10^-6 m 

θ = 18.42°

when λ = 700 nm = 700 * 10^-9 m

sin θ = 700 * 10^-9 m / 1.2658 * 10^-6 m 

θ = 33.57°

Therefore the range of angles is 18.42° to 33.57°.

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