光学显微镜

• Snell’s Law can calculate the focal spot of the glass sphere.
• Glass spheres are used to couple light into and from
optical fibers. Use Snell’s law and that is all!
we will not need to consider wave or E & M aspects of light
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Particle and Wave Properties of Light (Duality)
• Light propagates as a
• What’s waving? Electric & Magnetic fields* • Speed c = 3 x 108 m/s in vacuum * • Has a wavelength and frequency = c / f • Exhibits interference and diffraction effects
• For >> d (Physical Optics)
– use a “wave” description – single and double slits, interference, diffraction6
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Reflection at an interface
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近年来，光学显微镜得到了很大的发展：主要为 荧光标记 数字成像与分析 共焦显微镜
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The Realm of Geometrical Optics
QUANTUM OPTICS ELECTROMAGNETIC OPTICS WAVE OPTICS GEOMETRICAL OPTICS
Corner Cube
40o
50o
Problem: What is the direction of the reflected ray
50o 40o 40o
Application?
Put it on the moon!
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Snell’s Law n1 sin 1 n2 sin 2
• Wavelength = c / f • Energy E = h f = hc /
= (1239 eV-nm)/ (nm) • Visible light (400) to (700) nm
400 nm 3.1 eV (5 x 10-19 J )
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• f = frequency (~1015 Hz ) • h = Planck’s Constant 6.626 x 10-34 J-s • 1 electron volt (eV) = 1.6 x 10-19 J
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Example: Color, Energy and Wavelength
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Light propagates as a
• Light transfers energy to other objects like a particle (collisions)
– particles called “photons” * – Particle energy E = h f
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Refraction at a Surface
for paraxial rays (i.e. small angle, < 15 deg) :
n1 n2 so si
n2 n1 R
R
n1
n2
so
si
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Convergents: 1) biconvex, 2) plane-convex, 3) concave-convex Divergents: 4) biconcave, 5) plane-concave, 6) convex-concave
Байду номын сангаас1 2
n1
n2
taken from normal
for n2 > n1: ray bends towards normal
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note: these rays are NOT paraxial
h = 0.7 mm
h = 1 mm
The Power of Snell’s Law
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Paraxial Rays
We want to simplify the end results of light ray physics
We assume in the following equations that light rays make small angles with the “optic axis”
Rays vs Waves Description
When light passes through an opening (aperture) of width d
• For << d (Geometrical Optics)
– use a “ray” description * – mirrors, lenses, reflection, refraction
optic axis
15deg sin(.262 rad) 0.259 10 deg: sin(.175 rad) 0.174 5 deg: sin(.873 rad) 0.872 1 deg: sin(30.5 mrad) 30.5 E-3
30 deg: sin(.524 rad) .5 45 deg: sin(.785 rad) .707 11
Question: What is the direction of the reflected ray?
’
• Angles measured from surface normal; incident angle
Law of Reflection = ’
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