problem 1a:  A set of two glass plates is stacked one atop the other.
One end of the first plate raised by inserting a piece of paper
between the glass plates.  The other end of the glass plates are in
contact. The thickness of the paper (t) is unknown.  The length of the
plates is unknown.  The angle of incline is unknown.  Assuming that
light with a wavelength of 552nm (in a vacuum) strikes the set of
glass plates nearly perpendicular to the horizontal; derive in detail
an equation for the thickness of the paper(t) in terms of the
wavelength of the light thru the space between the plates
approximating that of the wavelength thru a vacuum.  Determine the
order(m) of bright fringes and list all numerical constants used.

problem #1b:  Assume the thickness of the paper in problem #1 (above)
is
4 x 10 to the negative 5th meters.  what is the number of bright
fringes observed from above?

problem #1c:  Referring to the setup in problem #1, explain why there
is a dark  fringe where the plates touch.

I need the answer by 08/05/02 before 8:AM

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Clarification of Question by guga-ga on 04 Aug 2002 16:12 PDT

my daughter gave me this question and I am trying to help her out I
don,t know if it is a science project (she takes summer classes).

Hi guga

I'm glad I got a chance to answer
this question. It did a good job of
knocking the rust off the physics
I took.


!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!


Problem #1a: Equation for the thickness
of the paper(t) in terms of the wavelength
of the light through the gap between the plates.

The thickness of the paper can be determined
by the order (number) of fringes from where
the plates touch to the edge of the paper,
with the wavelength known. The distance the
light must travel in the gap is round-trip. The
minimum path length difference is half a
wavelength.

Thus,
t = ((m + 1/2)(wavelength)) / 2

Where t = thickness of paper (unknown)

m = number of bright fringes to the paper
    or the order of bright fringes (unknown)

wavelength = 552nm


Determine the order (m) of bright fringes

The order of fringes (m) is relative to the 
distance from the point of contact of the
glass plates to the edge of the paper by:

m = (2t / wavelength) - 1/2

Where t = thickness of paper (unknown)

m = number of bright fringes to the paper
    or the order of bright fringes (unknown)

wavelength = 552nm


!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!


Problem #1b: Assume the thickness of the paper
in problem #1a (above) is 4x(10^-5)m meters, how
many bright fringes are observed.

The number of bright fringes (m) = twice the
thickness of the paper divided by the wavelength
minus one half. 

m = (2t / wavelength) - 1/2
where t = 4x(10^-5)m and wavelength = 552x(10^-9)m

So,
m = (2 x 4x(10^-5)m / 552x(10^-9)m) - 0.5 = 144.43
rounded we get 144. The first bright fringe
occurs at m = 0 so total bright fringes would
equal 145


!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!


Problem #1c: Explain why there is a dark
fringe where the plates touch. 

There is a dark fringe where the plates touch 
because of destructive interference at that 
point. This is caused by the phase shift upon
reflection of the wave reflected from the lower
plate at a distance of 0.


m = (2 * 0 /(552x(10^-9)m) - 1/2
m = -1/2 half-wavelength phase shift 



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[ http://131.128.120.24/PHY205/PHY205-HW/exam4/index.html ]

[ http://216.239.37.100/search?q=cache:tey7hn7mLL8C:niuhep.physics.niu.edu/~willis/phys251/chapter_27_day_1.html+glass+plates+angle+wavelength+light++fringe&hl=en&ie=UTF-8
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I sure hope this is correct, it looks
like I only get one shot at this. I had
a nice lil diagram all made up in Adobe
Illustrator... but I have no where to
upload it to, for you to publicly access it.


thanks for asking us this question
-AI

I rated you because you were fast in getting the ans.  and gave some
infor where to look. you are great.  also to let you know that I am
getting close to BIG 50 so I just don't have that energy to go back to
school. thanks