A
circular obstacle produces the same diffraction pattern as a circular
hole of the same diameter (except
very near ).
Airborne water drops are examples of such
obstacles. When we see
the Moon through suspended water drops, such as in a fog,
we intercept the diffraction pattern from many
drops; the composite
is a bright circular pattern surrounding the Moon.
Next to the Moon, the
pattern is white. (a) We
have to find the colour, red
or blue, that outlines
the white pattern. (b) We
may assume that the outlining ring has an angular diameter that is
1.5 times the angular diameter of the Moon,
which is.
We may also assume that the drops all have
about the same diameter. We
have to find the approximate value of the diameter.
When there
are many water droplets located randomly the net effect of
interference of light falling from the Moon will
be that of cumulative diffraction associated with a single droplet.
Let the diameter of droplets be
.
The condition on the angular size of the diffraction ring that is
the first diffraction minima is determined by the wavelength of
light
and the size of the droplet, both of which should be of the same
order. The angular size of the diffraction ring will be largest for
the visible light of the longest wavelength, which is red, and its
wavelength is 690 nm. Therefore, the colour of the outline around
the white diffraction pattern will be red.
(b)
The angular size of the
diffraction ring is given to be
The size of
water droplets can be determined by using the result that the first
diffraction minima of a circular drop of diameter
is related to the wavelength
by the equation
).
Airborne water drops are examples of such
obstacles. When we see
the Moon through suspended water drops, such as in a fog,
we intercept the diffraction pattern from many
drops; the composite
is a bright circular pattern surrounding the Moon.
Next to the Moon, the
pattern is white. (a) We
have to find the colour, red
or blue, that outlines
the white pattern. (b) We
may assume that the outlining ring has an angular diameter that is
1.5 times the angular diameter of the Moon,
which is
.
We may also assume that the drops all have
about the same diameter. We
have to find the approximate value of the diameter.
.
The condition on the angular size of the diffraction ring that is
the first diffraction minima is determined by the wavelength of
light
and the size of the droplet, both of which should be of the same
order. The angular size of the diffraction ring will be largest for
the visible light of the longest wavelength, which is red, and its
wavelength is 690 nm. Therefore, the colour of the outline around
the white diffraction pattern will be red.
.