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Chapter 5: Q28E (page 1213)

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.)

Short Answer

Expert verified
  1. The angular width of the visible spectrum in first order is7.55掳
  2. The angular width of the visible spectrum in third order is28.3掳

Step by step solution

01

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 is7.55掳

02

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 is28.3掳

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