Manufacturers of wire (and other objects of small dimensions) sometimes use a la

Question

Manufacturers of wire (and other objects of small dimensions) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction pattern like that of a single slit of the same width as the wire diameter (see Fig. 37-50). Suppose a laser of wavelength 646.3 nm, illuminates a wire, and the diffraction pattern appears on a screen 2.74 m away (do not use the number shown in the diagram). If the desired wire diameter is 1.21 mm, what is the observed distance between the two tenth-order minima (one on each side of the central maximum)?

Explanation / Answer

given data,

slit width, d = 1.21 mm = 1.21*10^-3 m

lamda = 646.3 nm = 646.3*10^-9 m

R = 2.74 m

distance from center of the screen to 10th minima = 10*lamda*R/d

so, distance between the two tenth-order minima (one on each side of the central maximum) = 20*lamda*R/d

= 20*646.3*10^-9*2.74/(1.21*10^-3)

= 0.0293 m or 2.93 cm <<<<<<<<<<-------------------Answer

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