1. (a) The condition for a minimum in a single-slit diffraction pattern is given by
a
sin
θ
=
m
λ
,
where
a
is the slit width,
λ
is the wavelength, and
m
is an integer. For
λ
=
λ
a
and
m
= 1,
the angle
θ
is the same as for
λ
=
λ
b
and
m
= 2. Thus,
λ
a
= 2
λ
b
= 2(350 nm) = 700 nm.
(b) Let
m
a
be the integer associated with a minimum in the pattern produced by light with
wavelength
λ
a
, and let
m
b
be the integer associated with a minimum in the pattern
produced by light with wavelength
λ
b
. A minimum in one pattern coincides with a
minimum in the other if they occur at the same angle. This means
m
a
λ
a
= m
b
λ
b
. Since
λ
a
= 2
λ
b
, the minima coincide if 2
m
a
= m
b
. Consequently, every other minimum of the
λ
b
pattern coincides with a minimum of the
λ
a
pattern. With
m
a
=
2, we have
m
b
= 4.
(c) With
m
a
=
3, we have
m
b
= 6.

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