Q28E - University Physics with Modern Physics

Question

The wavelength range of the visible spectrum is approximately 380 - 750 nm. White light falls at normal incidence on a diffraction grating that has 350 slits/mm. Find the angular width of the visible spectrum in (a) the first order and (b) the third order. (Note: An advantage of working in higher orders is the greater angular spread and better resolution. A disadvantage is the overlapping of different orders, as shown in Example 36.4.)

Step-by-Step Solution

Answer

1. The angular width of the visible spectrum in first order is $7.55°$
2. The angular width of the visible spectrum in third order is $28.3°$

Step 1: Determine the angular width of the visible spectrum in the first order

The width of the slit is

             

(a) The angular width in the case m = 1

                   

And,

           

Therefore, the angular width of the visible spectrum in first order is $7.55°$

Step 2: Determine the angular width of the third order

(b) The angular width in the case m = 3

         

And,

         

Therefore, the angular width of the visible spectrum in third order is $28.3°$