Question

Diffraction can be used to provide a quick test of the size of red blood cells. Blood is smeared onto a slide, and a laser shines through the slide. The size of the cells is very consistent, so the multiple diffraction patterns overlap and produce an overall pattern that is similar to what a single cell would produce. Ideally, the diameter of a red blood cell should be between 7.5 and 8.0 μm.

If a 633 nm laser shines through a slide and produces a pattern on a screen 24.0 cm distant, what range of sizes of the central maximum should be expected? Values outside this range might indicate a health concern and warrant further study.

Answer 1

From the formula of diffraction pattern,

y / L = m $\lambda$ / d

y = $\lambda$ L / d

Width of central maxima, w = 2y =  2 $\lambda$ L / d

for d = 7.5 um

w = 2*633*10^-9*24*10^-2 / 7.5*10^-6

w = 4.05 cm

for d = 8 um

w = 2*633*10^-9*24*10^-2 / 8*10^-6

w = 3.798 cm

Range of central maxima = 3.798 cm to 4.05 cm