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Light
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Indices of Refraction:
Quartz: 1.458
Glass, crown 1.52
Glass, flint 1.66
Water 1.333
Air 1.000 293
Angle of Incidence:
The angle measured from the perpendicular to the face or from the perpendicular to the tangent to the face
Index of Refraction: Materials of greater density have a higher index of refraction.
N º c/v
n=l0 / ln
n = index of refraction
c = speed of light in a vacuum 3 × 108 m/s
v = speed of light in the material [m/s]
l0 = wavelength of the light in a vacuum [m]
ln = its wavelength in the material [m]
Law of Refraction: Snell’s Law
N1 sinq1 = n2 sinq2
traveling to a region of lesser density: q2 > q1
n = index of refraction q= angle of incidence
traveling to a region of greater density:
q2 <q1
Critical Angle: The maximum
angle of incidence for which light
can move from n1 to n2
sinqc = n2 / n1 for n1 > n2
Sign Conventions:
When M is negative, the image is inverted. p is positive when the
object is in front of the mirror, surface, or lens. Q is positive when the image is in front of the mirror or in back of the surface or lens. f and r are positive if the center of curvature is in front of the mirror or in back of the surface or lens.
Magnification
by spherical mirror or thin lens. A negative m means that the image is inverted.
M = h’/h = - i/p
h’ = image height [m]
h = object height [m]
i = image distance [m]
p = object distance [m]
Plane Refracting Surface:
plane refracting surface:
(n1 / p) = -(n2 I )
p = object distance
i = image distance [m]
n = index of refraction
Lensmaker’s Equation for a thin lens in air:
R1 = radius of surface nearest the object[m]
R2 = radius of surface nearest the image [m]
f= focal length [m]
i = image distance [m]
p = object distance [m]
n = index of refraction
Thin Lens
when the thickest part is thin compared to p. i is negative on the left, positive on the right
f = r/2
Converging Lens
f is positive (left)
r1 and r2 are positive in this example
f = focal length [m]
r = radius [m]
Diverging Lens
f is negative (right)
r1 and r2 are negative in this example
Two-Lens System
Perform the calculation in steps.Calculate the image produced by the first lens, ignoring the presence of the second. Then use the image position relative to the second lens as the object for the second calculation ignoring the first lens.
Spherical Refracting Surface
This refers to two materials with a single refracting surface.
p = object distance
i = image distance [m] (positive for real images)
f = focal point [m]
n = index of refraction
r = radius [m] (positive when facing a convex surface, unlike with mirrors)
M = magnification
h' = image height [m]
h = object height [m]
Constructive and Destructive Interference by Single and Double Slit Defraction and Circular Aperture
Young’s double-slit experiment (bright fringes/dark fringes):
Double Slit
Constructive:
ΔL = d sinq = ml
Destructive:
ΔL =d sinq =(m+ ½)l
d = distance between the slits [m]
q = the angle between a normal line extending from midway
between the slits and a line extending from the midway point to the point of ray
Intensity:
intersection.
m = fringe order number [integer]
l = wavelength of the light [m]
a = width of the single-slit [m]
ΔL = the difference between the distance traveled of the two rays [m]
I = intensity @ q [W/m2]
Im = intensity @ q = 0 [W/m2]
d = distance between the slits [m]
Single-Slit
Destructive:
a sinq = ml
Circular Aperture
1st Minimum:
In a circular aperture, the 1st minimum is the point at which an image can no longer be resolved.
A reflected ray undergoes a phase shift of 180° when the reflecting material has a greater index of refraction n than the ambient medium. Relative to the same ray without phase shift, this constitutes a path difference of l/2.
Interference between Reflected and Refracted rays
from a thin material surrounded by another medium:
Constructive:
2nt = (m+1/2 ) l
Destructive:
2nt = ml
n = index of refraction
t = thickness of the material [m]
m = fringe order number [integer]
l = wavelength of the light [m]
If the thin material is between two different media, one with a higher n and the other lower, then the above constructive and destructive formulas are reversed.
Wavelength within a medium:
ln = l n
C= nlnf
l = wavelength in free space [m]
ln = wavelength in the medium [m]
n = index of refraction
c = the speed of light 3.00 × 108 [m/s]
f = frequency [Hz]
Polarizing Angle:
by Brewster’s Law, the angle of incidence that produces complete polarization in the
reflected light from an amorphous material such as glass.
tranqB = n2 / n1
qr + qB = 90°
n = index of refraction
qB = angle of incidence producing a 90° angle between reflected and refracted rays.
qr = angle of incidence of the refracted ray.
Intensity of light passing through a polarizing lense: [Watts/m2]
initially unpolarized: I = 1/2 I0
initially polarized:
I = I0 cos2q
I = intensity [W/m2]
I0 = intensity of source [W/m2]
q = angle between the polarity of the source and the lens.
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