1) A double-slit experiment is set up using red light ( = 723 nm). A first order

Question

1)

A double-slit experiment is set up using red light ( = 723 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?

=

nm

2)

A new experiment is created with the screen at a distance of 2.1 m from the slits (with spacing 0.1 mm). What is the distance between the second order bright fringe of light with = 681 nm and the third order bright fringe of light with = 406 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)

|x| =

m

Explanation / Answer

interference:
condition of bright fringe, yb = m*lambda*D/d
condition of dark fringe, yd = (m+1/2)*lambda*D/d
use:
yb = yd
m1*lambda1*D/d = (m2+1/2)*lambda2*D/d
m1*lambda1 = (m2+1/2)*lambda2
1*723 = (m2+1/2)*lambda2

if m2=1 that is for 1st order dark fringe:
1*723 = (1+1/2)*lambda2
lambda2 = 482 nm
Answer: 482 nm

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