An intern engineer is designing a set up based on diffraction to measure the dia

Question

An intern engineer is designing a set up based on diffraction to measure the diameter of thin wires. He tested the setup by using a known wire of diameter 0.02 mm. He used a coherent light source of wavelength 361 nm. He positioned the viewing screen 4.8 m from the wire.

a) What is in m the position of the first diffraction minimum due to the light?

b) What is in m the width ?ycentral of the central diffraction maximum?

c) What is in m the position of the second order diffraction maximum?

d) What is in m the width ?y of the second order maximum?

Explanation / Answer

given

wvelength,lamda = 361 nm

slit width, d = 0.02 mm 2*10^-5 m

distance from slit to screen, R = 4.8 m

a) for first dark fringe, y1 = lamda*R/d

= 361*10^-9*4.8/(2*10^-5)

= 0.0866 m

b) central bright fringe width = 2*lamda*R/d

= 2*361*10^-9*4.8/(2*10^-5)

=0.1732 m

c) fr second order difraction maximum = (3/2)*lamda*R/d

= 1.5*0.0866

= 0.13 m

d) width = 0.1732/2 = 0.0866 m

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