A Young\'s double-slit apparatus is set up. A screen is positioned 1.60 m from t

Question

A Young's double-slit apparatus is set up. A screen is positioned 1.60 m from the double slits and the spacing between the two slits is 0.040 0 mm. The distance between alternating bright fringes is 1.42 cm. What is the light source wavelength? (1 nm= 10^-9 m) a. 710 nm b. 490 nm c. 280 nm d. 355 nm If the 2nd order fringe in Young's double-slit experiment occurs at an angle of 45.0 degree, what is the relationship between the wavelength lambda and the distance between slits, d? a. d = 1.41 lambda b. d = 2.00 lambda c. d = 2.83 lambda d. d = 4.00 lambda

Explanation / Answer

Young's double-slit experiment

path difference = d*sintheta

for bright fringe

path difference = m*lambda

d*sintheta = m*lambda

for small angles sintheta = tantheta = y/R

d*y/R = m*lambda

y = m*lambda*R/d

d = slit width

m = order of bright fringe

R = distance between screen and slit

y = position of bright fringe on screen

for m = 1

y1 = lambda*R/d

for m = 2

y2 = 2*lambda*R/d

fringe width dy = y2 - y1

dy = lambda*R/d

1.42*10^-2 = lambda*1.6/(0.04*10^-3)

lambda = 355 nm <<<-----------answer

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4)

d*sintheta = m*lambda

d*sin45 = 2*lambda

d/sqrt2 = 2*lambda

d = 2*sqrt2*lambda

d = 2.83*lambda

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