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1) A double-slit experiment is set up using red light ( = 734 nm). A first order

ID: 1483708 • Letter: 1

Question

1)A double-slit experiment is set up using red light ( = 734 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 1.8 m from the slits (with spacing 0.08 mm). What is the distance between the second order bright fringe of light with = 682 nm and the third order bright fringe of light with = 403 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

here,

A.

theta = arcsin(m*lambda1/d),

where m = 1

theta = arcsin(m2*lambda2/d)

Thus lambda2 = lambda1/m2 ,

where m2 = 0.5, 1.5, etc (until lambda is within the specified range)

m = 1.5 works;

lambda2 = lambda1/1.5 = 489.33 nm

the wavelength of the visible light is 489.33 nm

B.

screen distance , D = 1.8 m

d = 0.08 * 10^-3 m

theta is small enough that we can use the small-angle approximation for deflection y.

y = m * lambda * D/d

for lamda1 = 682 * 10^-9 and m = 2

y1 = 2 * 682 * 10^-9 * 1.8 /( 0.08 * 10^-3)

y1 = 0.030690 m

for lamda2 = 403 * 10^-9 and m = 2

y2 = 2 * 403 * 10^-9 * 1.8 /( 0.08 * 10^-3)

y2 = 0.018135 m

the distance between them = y1 - y2 = 0.012555 m