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83 Cards in this Set
- Front
- Back
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Frequency =
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1/period
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The 2 equations for velocity are
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Velocity = 1/wavelength
Velocity = wavelength x frequency |
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The visible range of light is from
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400 nm - 750 nm
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Velocity in air / Velocity of a material =
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Refractive index
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Wavelength in air / Wavelength of a material =
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Refractive index
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What is the refractive index of water?
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1.3333
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What is the formula for Snell's law of refraction?
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nsinΘi = n'sinΘr
where Θi = incident angle Θr = refracted angle |
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A ray of light passing through air has an angle of incidence of 30 degrees upon a sheet of glass. What is the refracted angle?
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Θr = 19.47 degrees
n=1 n'=1.5 1(sin30)=1.5(sinΘr) sinΘr=.5/1.5 Θr = 19.47 degrees |
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What is the refractive index of glass?
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1.5
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Snell's Law: What is the critical angle?
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The critical angle (Θc) is the Θi that would give Θr = 90 degrees. It only exists if n>n'.
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Snell's Law:
Incident angles greater than the critical angle (Θc) result in what? |
Total internal reflection
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Snell's Law:
What is the formula for determining the critical angle? |
SinΘc = n'/n
The critical angle only exists if n>n'. |
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A ray of light in glass is incident upon water. What is the critical angle?
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Θc = 62.71 degrees
sinΘc= n'/n n' = 1.333 n = 1.5 sinΘc = .888667 Θc=62.71 degrees |
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A ray of light in glass is incident upon water. What is the minimum angle of total internal reflection?
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Θir= 62.72 degrees
Remember, any angle greater than the critical angle will cause total internal reflection. Therefore, we must use the formula and find the critical angle. sinΘc = n'/n n'=1.333 n = 1.5 sinΘc =.888667 Θc = 62.71 degrees Since the critical angle is 62.71 degrees, any angle greater will cause total internal reflection. |
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Total internal reflection is only possible when
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n>n'
The first medium has a higher index of refraction than the second. Examples: Light from glass into water Light from water into air Light from glass into air |
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What is the formula for curvature?
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Curvature (R) = 1/r where r=radius
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What is the definition of vergence?
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The vergence of rays at a certain point is the reciprocal of the distance from the point to the source.
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In air, Diopters =
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1/meters
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The formula for incident vergence (U)
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U= n/u
where n is the refractive index before refraction and u is the distance of the object to the surface or lens |
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The formula for emergent vergence (V)
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V= n'/v
where n' is the refractive index after refraction and v is the distance to the surface or lens |
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An object in air is 50 cm from a +5.00D lens. n' = 1.5 Where would the image be located?
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v = 0.50 m
U+D=V (1/-.50) + 5 = 1.5/v 3=1.5/v v= .50 m or 50 cm Remember, any object distance to the left of the lens (D) is a negative distance. Any object distance to the right of the lens is a positive distance. |
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What is the vergence of a wave front in air 27cm from the point source that generated it?
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V = -3.7 D
This is a simple vergence problem. U+D=V There is no lens, so D = 0 U = 1/-.27 = -3.7D -3.7D +0 = V V=-3.7D |
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Convergent light in air leaves an optical system with a vergence of +3.33D. What is the vergence of the wave front 10cm to the right of the optical system.
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V= 5 D
The wavefront comes into focus at 1/3.33 = 30cm to the right of the optical system. At 10cm to the right of the optical system, the wavefront has a vergence of V= n/v = 1 (.3-.1)m = 1/0.2 = 5 D |
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The screen of a pinhole camera is 20mm from the pinhole. The screen is 1.5 cm in height. If a picture of an object 3m tall is to be taken and the image is to fill the screen what is the screen-to-object distance?
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u+v= 4.02 m
Using similar triangles, 3m/.015m = 200 The object is 200x bigger than the screen. Therefore, the length between the object and the pinhole has to be 200x the length between the pinhole and the screen. Since v (length between pinhole and screen) is .02m, then u (length between object and pinhole) has to be 4 m. Remember, the question is asking for the length from the object to the screen. u+v 4+.02=4.02 |
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The object for a pinhole camera is located 50 feet from the pinhole, and its size is 30 times that of the image. What is the screen-to-pinhole distance?
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v= 1.66 feet
50/30= 1.66 feet |
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What is the formula to determine the dioptric power of a surface?
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(n'-n)/r
where r is the radius of curvature |
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What are the primary and secondary focal lengths in a +5.00D surface with n'=1.5?
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f = -.2 m
f ' = .3 m D = -n/f = n'/f ' 5 = -1/f f = -.2 5 = 1.5/f ' f ' = .3 |
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What is the dioptric power of a lens if f = -.2m and f ' = .3m? n' =1.5
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D=5D
r = f+f ' r = -.2+.3 r = .1 D = (n' - n)/r D = (1.5-1)/.1 D=5 |
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What is the definition of F (the anterior or primary focal point)?
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The anterior or primary focal point (F) is the object point conjugate to an image at infinity.
f = n/F f = anterior (primary) focal point distance |
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What is the definition of F' (the posterior or secondary focal point)?
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The posterior or secondary focal point (F') is the image point conjugate to an object at infinity.
f ' = n'/F' f ' = posterior (secondary) focal point distance |
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What are the first 3 points to determine when ray tracing?
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F, F', and N
F = Object point conjugate to an image at infinity F' = Image point conjugate to an object at infinity N = Center of curvature |
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How do you determine the center of curvature in a SSRS?
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D = (n'-n)/r
r = center of curvature |
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A real object emits ________ rays.
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Divergent
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A virtual object "emits" __________ rays.
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Convergent
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Draw a ray trace. Describe the image as real/virtual, erect/inverted, and the size relative to the object. Where is the image located?
n = 1, D = +4, n' = 1.5, u = -0.5 m |
Image is real, inverted, and y'y = 1.
The image is 0.75 cm to the right of the SSRS. |
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What is the formula for magnification?
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U/V = m
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What does a negative magnification mean?
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It means the image is inverted.
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A biconcave thin lens in air has a real object. The image is 20cm from the object and is 1/3 its size. What is the power of the lens?
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D = 6.67D
m=U/V m = v/u .333 = .20/u u = -.6006 U = -1.665 D V = 5 U+D=V -1.665+D=5 D= 6.67D |
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Minus lenses are ______, plus lenses are ______.
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Concave, Convex
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A thin lens is made of glass. rF = 10cm, rB = 5cm. What is the Df, Db, and D?
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Df= +5D
Db= -10D D= -5D (1.5-1)/(.1m) = +5D (1-1.5)/(.05m) = -10D 5-10 = -5 D |
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What is the lens effective power formula?
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Deff= D/(1+dD)
Where D is the power of the lens and d is the distance moved. d is + when the lens is moved in the direction of light travel. |
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What is the new effective power of a +10.00 D lens 5 cm to the right, just after you move the lens 5 cm to the left?
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Deff = +20.00D
Deff= 10/(1+ (-.05*10)) = +20.00D |
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As you move a lens away from your eye, you _______ the lens' plus power and ________ the lens' minus power
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Increase, Decrease
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What is the effectivity formula?
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Effectivity = D/(1-dD)
Note: this is similar to the lens effective power formula, but since we are bringing the lens away from our eye, and therefore away from light travel, you have to use a - . |
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How is ray tracing for a thin lens different than ray tracing through a SSRS?
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The N goes through the center of the lens instead of the radius of curvature.
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What is the circle of least confusion?
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The circle of least confusion, also known as the blur circle, is the point of best focus for the entire lens, To find it take the reciprocal of the average power of the 2 principle meridians.
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Your spectacle Rx is +4.00-2.00x180. Where is the circle of least confusion?
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CLC = .333 m
(4.00+2.00)/2 = 3 1/3 = .333m |
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What is the interval of Sturm?
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The interval of Sturm is the distance between the two foci of the principal meridians.
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Your spectacle Rx is +4.00-2.00x180. What is the interval of Sturm?
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IS= .25 m
1/4 = .25 m 1/2 = .50 m .50-.25 = .25 m |
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How do you determine the amount of prism induced in a lens?
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P = (d)(D)
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Define a prism diopter.
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One prism diopter is the amount of prism required to deviate a light 1 cm at a distance of 1 meter.
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The image moves towards the ______.
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apex
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What is the formula for the deviation for light passing through a thin prism in air?
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d = (n-1)A
where n is the refractive index of the prism, and A is the apex angle |
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What is the deviation for a thin glass prism with a 5 degree apex angle? Convert this into prism diopters.
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D = 2.5 degrees
In prism diopters = 4.4D (1.5-1)(5) =2.5 tan(2.5) = x cm/100 cm x = 4.4 cm |
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A 5 D myope with a 58 mm PD views through a pair of spectacles with the optical centers 64 mm apart. What is the total prism power the myope looks through?
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Prism = 3 BI
(.64-.58)5 = 3 BI Remember how to diagram prism for plus or minus lenses. A 5 D hyperope would have been 3 BO. |
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What is longitudinal spherical abberration?
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The axial distance between marginal ray focus and paraxial ray focus.
Marginal rays focus closer to the lens and in front of paraxial rays. |
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What is the formula for spherical abberration?
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Sphabb = Vm-Vp
Where Vm = Vergence of marginal rays and Vp = Vergence of paraxial rays |
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A +20D lens has a power of +20.50D at a distance of 10mm from the center. What are the longitudinal and lateral SA for a distant object?
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SAlong = 1.2 mm
SAlat = 0.2 mm Draw it out! 20.50-20=.50D (1/20)-(1/20.50) = 1.2mm = SAlong Use similar triangles x/1.2 mm = 10/48.8 x = 0.2 mm Basically, you are pretending that there are 2 different lenses, but are superimposing them on the same line. The question is asking you what is the difference between their two focal points (long) and what is the difference in the image size (lat). |
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What is coma?
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Coma is a type of spherical aberration for off-axis objects. Intermediate zones between the center of lens and the peripheral lens are imaged a smaller circles between the two points.
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What is oblique astigmatism?
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Oblique astigmatism occurs when a bundle of rays meets a lens surface obliquely, and the beam forms an ellipse with a shorter tangential axis and a longer sagittal axis.
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How do you determine the new cylinder power when you tilt a lens?
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Pc = D (tan^2(f))
Where Pc is new cylinder power D is the sphere power f is the angle of lens tilt |
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When you tilt a plus lens you get ______ cylinder. When you tilt a minus lens you get ________ cylinder.
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Plus, Minus
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How do you determine induced sphere power of a tilted lens?
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Is = (Dsin^2(f))/2n
Where Is = induced sphere power D = originial sphere power f= angle of lens tilt n = index of refraction SHORTCUT: INDUCED SPHERE IS ABOUT 1/3 INDUCED CYLINDER |
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What is the effective Rx if a +10D spectacle is worn with a panascopic tilt of 15 degrees?
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=10.24+0.72x180
=10tan^2(15) =0.72 0.72/3 = 0.24 0.24+10 = 10.24 Remember, a plus lens creates plus cylinder, a minus lens creates minus cylinder. |
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What is the formula for sag?
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S= D(h^2)/2(n'-n)
where D is the power of the lens h is the distance between the end and middle prong of a lens clock |
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What is the minimum thickness for a minus lens safety lens?
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3 mm
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What is the minimum thickness for a plus lens safety lens?
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2.5 mm
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What is the minimum edge thickness for safety lenses?
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2.5 mm
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What is the formula for edge thickness?
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= Sag + center thickness for minus lenses
and Sag - center thickness for plus lenses So... (D(h^2)/2(n'-n)) + or - center thickness |
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If a frames A size is 31 and DBL is 9, what is the frame pd?
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Frame pd = 40
Frame pd = A + DBL |
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How do you determine the minimum blank size for a lens?
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MBS = ED + 2(decentration)
where ED is the longest dimension of the lens. |
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What is the formula to determine the lens power from a lens clock reading?
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r = (h^2 / 2s) + (s/2)
n/r = D where h is the distance between the first and middle pin of the lens clock and s is the sag or center thickness |
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What is the refractive index of polycarb?
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1.586 D
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What is the formula for sag?
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sag = Dh^2/2(n'-n)
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How do you determine sag when you know the edge thickness and the center thickness of a lens?
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sag = ct - et
where ct is center thickness and et is edge thickness |
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When picking a lens for a high hyperope or myope, the lens should have a _____ shape.
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round
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What is the law of reflection?
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In planar mirrors, incident angle = reflected angle
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In spherical mirrors, convex mirrors ________ light and concave mirrors _________ light.
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Diverge, Converge
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What is Fresnel's Law?
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The proportion of light reflected from a mirror is
% reflected = (n2-n1/n2+n1)^2 x 100% |
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How do you determine the focal power of a mirror?
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D = (n2-n1)/r
D = -2n/r |
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A real object is 40 cm away from a convex mirror of radius 33.3 cm immersed in water. Perform a ray trace and describe the image.
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Image is virtual and erect, v = -12 cm
m = .333 |
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In mirrors, real objects and real images are ________ while virtual objects and virtual images are ________.
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negative, positive
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What is the total power of a lens mirror made up of a +4.00 biconvex lens?
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Dt = 15.65 D
Remember, you have to find out the power of reflectance and add it to the 2 refractions. Reflectance is determined by Dm = -2n/r Use the back surface of the mirror to determine r. D = (n'-n)/r Then add that to 2x the refraction of the first surface. Df = 2(D1) + Dm D1 = +2.00 D2 = +2.00 +2.00 = (1-1.5)/r r = -26.15 cm Dm = -2n/r = -2(1.5)/-.2515 = 11.98 Dt = 2(2) + 11.65 = 15.65 |
