Question

Problem 2: A 21-W horizontal beam of light of wavelength 430 nm, travelling at speed c, passes through a rectangular opening of width 0.0048 m and height 0.011 m. The light then strikes a screen at a distance 0.36 m behind the opening.

a) The quantity NO that you found in part (d), which is 1.58 x 10^18, gives the rate at which photons enter the region between the opening and the screen. Assuming no reflection from the screen, find the number of photons in that region at any time.

b) How would the number of photons in the region between the opening and the screen change, if the photons traveled more slowly? Assume no change in any other quantity, including the speed of light.

Answer 1

a) number of photons in region, n = (rate of photons entering) ( length) / speed of photons
      n = 1.58 x 10¹⁸ (sec^-1 ) * 0.36 m / 3x10⁸ m/s
         = 1.90 x 10⁹

b) As number of photons in the region are inversely proportional to speed of photons, number of photons will be more if if photons travel more slowly.