Hi Monga,
I am still not 100% sure about part (b), since it sounds pretty much
identical to what you're asking in (a) (see below). So I've decided to
post my answer as a comment, if you are satisfied tell me and I will
re-post this as an answer, or if you still want more for part (b) tell
me more precisely what you mean and I'll see what I can do.
I've used formulas and explanations for the Fabry-Perot Interferometer
which appear in the site
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fabry.html
This site has very nice pictures and explanations and I recommend that
you take a look at it if you're interested.
You have given me the following data: The reflectance r of the mirrors
is 0.95; The separation between the mirrors is d=0.1 mm. Another
number that we will need in order to calculate the separation between
wavelengths is m, the so-called order of interference. I must confess
I did not understand very well what it is (I am a mathematician with a
strong physics background, but interferometers are not my specialty),
but it is given approximately by the expression 2*d/lambda, provided
that the angle of the incident light is small (which I assume is
satisfied if the interferometer is used correctly). lambda is the
wavelength, in our case 600nm.
So we have: r = 0.95; d = 0.1 mm; lambda = 600 nm;
m = 2d/lambda = 2 * 0.1*10^(-3) m / (600*10^(-9) m) = 333.33
Finally, the possible change in wavelength that the intereferometer
can detect is given by
delta(lambda) = lambda * (1-r) / (m * pi * sqrt(r)) =
= 600 nm * 0.05 / (333.33 * 3.14159 * sqrt(0.95)) =
0.02939 nm
(This is what I mistakenly called the "resolvance" in my earlier
request for clarification. In fact the resolvance is defined as the
ratio
lambda/delta(lambda))
In other words, at a wavelength of 600.0 nm, the interferometer can
separate two adjacent wavelengths provided that the difference in
their wavelengths is at least 0.029 nm. In your example 600.0 nm and
600.1 nm have a difference of 0.1 nm, which is greater than this
number, so the interferometer WILL in fact be able to separate them.
On the other hand, you write
"Some of the components of this spectrum have a wavelength difference
of only 0.002nm"
"(a)Calculate whether the interferometer will be able to
distinguish between the components having a wavelength difference of
0.002nm."
So for this question the answer is "No", since 0.002 nm is clearly
lower than the threshold of 0.029 nm.
Now for part (b):
"(b)Calculate whether there will be overlap between the various
orders of the spectra fromed by the interferometer."
If I understand this correctly - and this is by no means certain -
this is the same as saying "Will there be overlap between the two
adjacent wavelengths?" (in this example 600.0 and 600.1 nm, although
you refer also to a wavelength difference of 0.002 nm)
The thing I am not sure about is whether this question is identical to
the question "Can the interferometer distinguish these two
wavelengths?"
Why am I not sure? Certainly, if the interferometer does NOT
distinguish between the two wavelengths, this means that there is
overlap. But, is it possible that two wavelengths may have some small
overlap but are still clearly distinguishable? I would tend to say
"no", in which case the answer to part (b), for the specific example
of 600.0 and 600.1 nm, is that there will be no overlap, since the gap
that we calculated, of 0.02 nm, is smaller than the difference of 0.1
nm. However, this is where my understanding of interferometers comes
to an end. Perhaps someone will care to comment?
I hope this is the answer you were looking for,
dannidin |
