Geometrical Optics:
Geometrical Optics & Physics Optics.
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Huygens Principle:
Wavefronts.
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Reflection:
The first law of Geometrical Optics.
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Refraction:
The second law of Geometrical Optics: Snell's law.
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Critical angle:
Internal total reflection.
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images formed by reflection
Spherical concave mirrors. Mirror equation.
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images formed by refraction
Spherical convex mirrors ..
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Fermat's principle:
Fermat's principle for reflection and refraction..
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lenses:
Thin lenses and Lens-makers' equation ..
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prism:
Prism, colors minimum deviation ..
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Human eye:
near point, far point, nearsightedness, farsightedness..
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Microscope:
Microscope: simple, compound, and magnification..
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Telescope:
Telescope: magnification..
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Resolution:
optical microscope, electron microscope ..
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dispersion:
dispersion, more about the refractive index, and colors of a prism ..
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parallel sheet:
deviation by a parallel sheet ..
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thin films :
thin films and Newton's rings..
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Newton's rings:
thin films and Newton's rings..
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Descartes rainbow:
Primary and secondary rainbows ..
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Some applications
More fun with Optics ..
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Optics calculator:
Optics calculator: all the related calculations ..
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home
The fundamental, and just this ..
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scientificSentence
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Geometrical Optics: Applications: Newton's rings
Optics -
Geometrical Optics..
1. Newton's rings
The device to prodice Newton's rings contains
A flat surface, a convex lens (spherical surface) with
an air wedge formed between them. The lens is
illuminated with normally incident monochromatic light (ray 1). The
circular fringes viewed are concentric circles around the point of
contact with the flat surface.
R is the radius of curvature of the lens,
T is the thickness of the lens where we
choose r.
Pythagorean theorem gives:
r^{2} + (R - t)^{2} = R^{2}
Therefore
r^{2} + t^{2} - 2 R t = 0
Because it is small, we neglect the term t^{2} , hence:
r^{2} = 2 R t , or
t = r^{2} /2R
t = r^{2} /2R
(1)
At the point A, th reflected ray does not undergo a phase change, but
at the point B the reflected ray 2 undergoes a π phase change.
Therefore
Δφ = φ3 - φ2 = (φB + φ(t)) - φA
The path difference between reflected rays is δ = 2t
φ(t) = 2 π δ/λ = 4 π t/λ
Hence:
Δφ = (π + (4πt/λ)) - o =
π(1 + (4t/λ))
1.The bright fringes corresponds the constructive
interferences and a phase difference of 2 m π. That
is:
2 m π = π(1 + (4t/λ))
Hence:
2 m = (1 + (4t/λ)), or:
t = (2 m - 1)λ/4
t = (2 m - 1)λ/4
(2)
2. The dark fringes corresponds the desstructive
interferences and a phase difference of (2 m + 1) π. That
is:
(2 m + 1) π = π(1 + (4t/λ))
Hence:
2 m = 4t/λ), or:
t = mλ/2
From equation (1), the radius r of the m-th ring corresponds to the
thickness of the air wedge t :
r = (2 R t )^{1/2}
The bright m-th ring corresponds to
r = (2 R t )^{1/2} = [R (m - 1/2)λ]^{1/2}
(3)
The dark m-th ring corresponds to
r = (2 R t )^{1/2} = (R mλ)^{1/2}
(4)
The bright m-th ring corresponds to:
r = [R (m - 1/2)λ]^{1/2}
The dark m-th ring corresponds to:
r = (R mλ)^{1/2}
Remarks:
1. The index of refraction of the lens has no importante.
2. The index of refraction of air is n = 1 that gives:
λ (in air) = λ(in vacuum) = λ

2. Example
If the incident light has a lambda; = 500 nm, and R = 2.00 m,
what is the radius of the 4th bright ring ?
r = [R (m - 1/2)λ]^{1/2} =
[2.00 (4 - 1/2)5 x 10 ^{-7>} ]^{1/2} =
18.71 x 10 ^{-4>} m = 1.9 mm.