In
the front of a lecture hall, a coherent beam of monochromatic light
from a helium-neon laser
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Solution: Click For PDF Version (a)A mirror has been kept at a distance of 20.0 m from the double slit. Thus image of the slits is formed at a distance of 20.0 m behind the mirror. As the interference pattern is observed on a screen facing the mirror, the effective distance of the screen from the virtual images is 40.0 m. The distance between the interference maxima will be given by the double-slit condition
where d
is the distance between the slits, and D
is the distance from the slits to the screen. As we have stated
above, in the experimental set up described in the problem
(b)
When
cellophane that contains 2.5 more waves than a path through air of
the same geometric thickness is inserted in front of one of the
slits, the phase difference between the rays changes by
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illuminates a double slit. From there it
travels a distance of 20.0 m to
a mirror at the back of the hall, and
returns the same direction to a screen. (a)
We have to fix the distance between the two
slits in order that the distance between the interference maxima is
observed to be 10.0 cm. (b) We
have to state the change in interference pattern if the lecturer
inserts in front of one of the slits a cellophane
that contains 2.5 more
waves than a path through air of the same geometric thickness.
,
.
We want
for laser light of wavelength
.
We thus find that
.
As a result in the interference pattern maxima and minima get
interchanged.