Diffraction
1)
The
distance between the first and fifth minima of a single-slit
diffraction
pattern is 0.35 mm with the screen
40 cm away from the slit, when light of wavelength 550 nm is
used.
(a)
Find
the slit width.
(b)
Calculate the angle θ of the
first diffraction
minimum.
2)
A
slit 1 mm wide is illuminated by light of wavelength 589 nm. We see a diffraction pattern
on
a
screen
3
m
away. What is the
distance between the first two diffraction minima
on
the
same
side
of
the
central diffraction maximum
?
3)
(a) Show
that
the values of α at which
intensity maxima for single slit diffraction occur
can
be
found
exactly
by
differentiating
the intensity formula (below) with respect
to
α
and
equating the result to
zero,
obtaining the condition tanα = α.
where,
(b) Find the
values of α satisfying this relation by
plotting the
curve y = tan α and the straight
line y = α and finding their
intersections or by using a calculator to
find an
appropriate value of α by trial
and error.
(c) Find
the (non-integer) values of m corresponding to successive
maxima in the single
slit
pattern. Note that the
secondary maxima do not lie exactly halfway between
minima.