A diffraction grating casts a pattern on a screen located a distance L from the

Question

A diffraction grating casts a pattern on a screen located a distance L from the grating. The central bright fringe falls directly in the center of the screen. For the highest-order bright fringe that hits the screen, m = x, and this fringe hits exactly on the screen edge. This means that 2x + 1 bright fringes are visible on the screen. What happens to the number of bright fringes on the screen (a) if the wavelength of the light passing through the grating is doubled and (b) if the spacing d between adjacent slits is doubled?

Explanation / Answer

Bright fringes occurs for m where

sinm = m/d

(a) If wavelength is doubled, number of non central bright fringes will reduce to half, so total bright fringes = x + 1

(b) If spacing is doubled, number of non central bright fringes will double, so total bright fringes = 4x + 1

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