Day 5 (1): Optics Flashcards

1
Q

Why does refraction of light happen?

A

REFRACTION

  • bending of light
  • light SLOWS down as it cross a DENSER medium with HIGHER index of refraction
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2
Q

What two variables affect the refraction of light?

A
  1. Difference in Index of Refraction between two media

2. Curvature of the optical medium

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3
Q

What is the index of refraction?

A
  • A dimensionless number that gives the indication of the LIGHT-BENDING ABILITY of that medium.
  • Determines how much the path of light is bent, or refracted, when entering a material.
  • Described by SNELL’S LAW OF REFRACTION

HIGHER index = DENSER medium = SLOWER speed of light = light is bent TOWARDS the normal line AWAY from surface = angle of refraction DECREASES

LOWER index = LIGHTER medium = FASTER speed = light is bent AWAY from normal line TOWARDS the surface = angle of refraction INCREASES

Normal line: an imaginary line perpendicular to the surface of the medium

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4
Q

What is Snell’s Law of Refraction?

A

Formula: n sin i = n’ sin r
Where:

n: index of refraction of medium 1
i: angle of incident ray from the normal line
n’: index of refraction of medium 2
r: angle of refracted ray from the normal line
Normal line: imaginary line perpendicular to the interface

i = r : NO refraction or bending, equal IoR
i > r : (+) bending TOWARDS normal line, IoR1 < IoR2
i < r : (+) bending AWAY from normal line, IoR1 > IoR2

  • Governs or describes the bending of light rays as they travel from one medium to another
  • E.g. as light travels from air (lower IoR) to water (higher IoR), light is bent CLOSER to the normal line and AWAY from the medium interface
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5
Q

What are the common refractive indices of the parts of the eye?

A

Air: 1.000
Tears, Aqueous, Vitreous: 1.336
Cornea: 1.376 (Keratometric: 1.338)
Lens: 1.420

Interfaces:
Air-Tear Film: 44 D (1.000 --> 1.336)
Tear Film-Cornea: 5 D (1.336 --> 1.376)
Cornea-Aqueous: -6D (1.376 --> 1.336)
Total: 43 D ~ 2/3 or 70% of refractive power of eye

Aqueous-Lens: 20 D (1.336 –> 1.420)
- 1/3 or 30% of refractive power of eye

Grand Total: ~ 60 D

Dioptric/Refractive Power of a medium

  • Determined by the difference in refractive indices of the mediums
  • Largest power or greatest bending of light happens when light enters the eye FROM AIR TO THE CORNEA due to the huge difference in IoR between the two
  • Because of the gradually increasing IoR between the media light passes through, it gets focused closer to the midline/macula
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6
Q

Difference between vision UNDER water and vision LOOKING DOWN on water.

A

Under water:

  • Since both observer and object are in SAME medium, NO refraction of light is happening
  • Location of objects are as they appear to be

Looking down on water:

  • Air-Water interface: 1.00 vs 1.33
  • Light travels faster in air (AWAY from midline and CLOSER to surface) because of the lower IoR
  • Brain assumes that all light rays travel in a straight line hence the location of the object is NOT SIMILAR to location of image
  • When looking at objects in the water, objects appear closer to surface but is in reality DEEPER
  • Thus: when trying to hit a target under water, angle the trajectory BELOW the image.
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7
Q

What are prisms?

A

Transparent triangular refracting medium with a BASE and an APEX where:

  1. Light is refracted towards the BASE
    - Air-Prism-Air interfaces: differences in index of refraction causes light to refract towards the base of the prism
  2. Apparent image is deviated towards APEX
    - Resultant refracted light rays are perceived by the brain as travelling in a straight line coming from near the apex

Prism Power: prism’s ability to deflect or bend light
- determined by the PRISM ANGLE of the APEX

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8
Q

How are prisms and lenses related?

A

Positive/Convergent/Convex Lens

  • two prisms with bases apposed to each other
  • focuses light rays towards a point at the RIGHT of the lens = REAL IMAGE

Negative/Divergent/Concave Lens

  • two prisms with apices apposed to each other
  • focuses light rays towards an imaginary point at the LEFT of the lens = IMAGINARY IMAGE

Prism Power vs Lens Power

Prism Power
- a measures the ability of a prism to change the path of light

Lens Power
- a measure of the ability of a lens (two prisms placed end to end) to converge or diverge light to a single point

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9
Q

What is the Prentice Rule?

A
  • A prism of 1 PRISM DIOPTER POWER produces a 1 CM apparent DISPLACEMENT of an object 1 M AWAY.
  • Determines the amount of prism power in a lens
  • Relates prism power to the lens power

PP (D) = decentration distance (cm) x LP (D)

  • The prism power of a lens at any point on its surface is the distance of the lens center from the optical center multiplied by the power of the lens
  • The HIGHER the lens power or the FARTHER away the lens center is from the center of the pupil, the HIGHER the prism power
  • When the center of the lens is aligned to the optical center (center of pupil), no matter how high the lens power is, the amount of prism is still ZERO

Conclusions:

  1. Prism is only induced when center of the lens IS NOT ALIGNED with the center of pupil (DECENTRATION)
  2. You can have lens power WITHOUT prism when centers are aligned.
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10
Q

How does the brain handle prisms?

A
  • When prismatic correction is placed in front of on eye, it affects both eyes because the brain applies it binocularly
  • Both eyes work in tandem to produce binocular vision
  • Thus, when applying prismatic correction, prims can be applied only to one eye OR split between both eyes
  • This balances the added weight and thickness of prism between the two lenses.
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11
Q

Optical center of the lens vs Optical center of the eyes?

A

Optical center of the eyes: center of the pupil

Optical center of the lens: central point of the lens/frame
- point which lies along the principal axis through which rays of light pass straight through WITHOUT refraction

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12
Q

Describe the prismatic effect of lens decentration.

A
  • Prism occurs whenever there is a difference in lens thickness between two points in the lens
  • Because lenses with power always have a variation in lens thickness, lenses always produce a prismatic effect
  • If center of lens and center of pupils are aligned, NET prismatic effect is ZERO because prismatic effect in other points of the lens allows light to focus towards the optical center = CLEAR image
  • If decentered, resultant net prismatic effect will NOT focus all light into the center of the pupil and into the macula = BLURRED image

Clear image:

  • distance between the centers of the two pupils should approximate the distance between lens centers
  • pupillary center aligns with the optical center
  • NO prismatic effect

Blurred image + eye fatigue + focusing error

  • (+) decentration or the pupillary centers are not aligned with the optical centers
  • Prismatic effect INDUCED

Note:

  • Decentration can be useful if the geometric center of the frame does not coincide with the center of the pupils.
  • Lens center is decentered from the frame center so that it would coincide with the center of the pupil.
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13
Q

Describe the base direction of the induced prismatic effect of decentered lenses.

A

Remember: prisms bend light towards BASE.

Lens center at pupil center: NO induced lateral prism
But at any point away from the optical center:

Positive/Convex/Convergent Lenses

  • thicker at center, thinner at edge
  • prismatic effect TOWARDS center
  • SAME direction as decentration:

(+) Lens with wide OC (OC > PD)
- decentration OUTwards = base OUT prismatic effect

(+) Lens with narrow OC (OC < PD)
- decentration INwards = base IN prism

Negative/Concave/Divergent Lenses

  • thinner at center, thicker at edge
  • prismatic effect AWAY from center
  • OPPOSITE direction as decentration:

(-) Lens with wide OC (OC > PD)
- decentration OUTwards = base IN prism

(-) Lens with narrow OC (OC < PD)
- decentration INwards = base OUT prism

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14
Q

What is vergence?

A
  • Describes how light rays behave relative to one another

Negative/DIVergence (<)

  • light rays move AWAY from each other
  • near light source
  • light becomes less bright with distance because beams become farther apart
  • ALL light in nature are diverging
  • E.g. flashlight

Positive/CONVergence (>)

  • light rays move TOWARD each other
  • becomes brighter because beams are concentrated
  • not naturally-occurring
  • E.g. laser

Zero Vergence (=)

  • light rays are PARALLEL to each other
  • far from light source
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15
Q

How is vergence quantified?

A

Formula:
Vergence (D) = 1/Distance (m)

  1. Unit: DIOPTERS
    - Negative because light is divergent
  2. Quantified based on the angle between light rays
    - The larger the angle, the more divergent or convergent the rays are
  3. Remember: light is created in a DIVERGENT manner from a single point source and spreading in all directions
    - As DISTANCE from source increases, VERGENCE decreases = LESS divergent
    - As distance approaches INFINITY, vergence becomes ZERO = PARALLEL
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16
Q

Relate vergence to visual acuity testing in the clinic.

A

At near: check how eyes respond to DIVERGING light

At distance: check how eyes respond to PARALLEL light

17
Q

What are convex lenses?

A

Positive/Convex/Convergent Lenses

  • two prisms with bases apposed to each other
  • corrects HYPEROPIA (light rays focus behind retina)
  • converges the light rays anteriorly into the retina
  • positive because real image is formed at the right of the lens
18
Q

What are concave lenses?

A

Negative/Concave/Divergent Lenses

  • two prisms with apices apposed to each other
  • corrects MYOPIA (light rays focus in front of retina)
  • converges the light rays back into the retina
  • negative because imaginary image is formed at the left of the lens
19
Q

What is the Basic Lens Formula?

A
  • U + D = V where,

U: vergence of light entering the system
- always NEGATIVE because at the LEFT of the lens and light is always DIVERGING
D: lens power/vergence
V: vergence of light exiting the system

Assuming U = 0 (entering light is parallel from an object located at distance infinity):
D = V (Lens Power = vergence of light exiting)
D = 1/Distance

E.g.
1. If you want to focus light 0.5 m away from lens:
D = 1/0.5 m = 2 D lens
2. Using a 4 D lens, how far from the lens will light focus: Distance = 1/4 D = 0.25 m or 25 cm

Thus: the HIGHER the power of the lens, the CLOSER the image will be.

20
Q

What are spherical lenses?

A
  • Lenses cut from a glass SPHERE
  • Focuses beam of light to a POINT (no axis or orientation)
  • Curvature and lens power is the SAME in ALL MERIDIANS
  • Can either be:
    1. Convex/Positive/Converging: add + vergence to light
  • forms a real image at the RIGHT side of the lens
    2. Concave/Negative/Diverging: adds - vergence to light
  • forms an imaginary image at the LEFT side of the lens
21
Q

What is the Primary Focal Point (F1) or the Object-Space Focus?

A

Point at which an object must be placed for PARALLEL rays to emerge from the lens and form an image at INFINITY

Plus/Convex Lens (-U + +D = 0)

  • point from which incident light must originate from to emerge PARALLEL
  • object at real point F1 (left of lens hence negative)
  • image at INFINITY

Minus/Concave Lens (+U + -D = 0)

  • point towards which incident light must be directed to emerge PARALLEL
  • object at imaginary point F1 (right of lens hence positive)
  • image at INFINITY
22
Q

What is the Secondary Focal Point (F2) or Image-Space Focus?

A

Point where PARALLEL incident rays are brought to a focus.

Plus/Convex Lens (0 + +D = +V

  • point where PARALLEL rays from a distant object converge
  • object at INFINITY
  • image at real point F2 (right of lens hence positive)

Minus/Concave Lens (0 + -D = -V)

  • point from which diverging rays seem to come from after a PARALLEL bundle of rays are refracted
  • object at INFINITY
  • image at imaginary point F2 (left of lens hence negative)
23
Q

What is the focal length?

A

Distance from the lens to the secondary focal point F2
Measure: Meters
Reciprocal of the dioptric power of the lens

F = 1/D

Identical to the vergence formula but:
- F2 assumes object is at infinity and incident rays are parallel (0 + D = V –> D = V –> D = 1/F)
-

24
Q

What is the lens power?

A
  • Describes how effective a lens is at focusing light towards a single point
  • Determined by the curvature of the lens
  • Distance of the lens to where light is focused as a point or a line
  • Unit: Diopters
  • Left side: MINUS space
  • Right side: PLUS space
  • Parts of the lens system:
    1. Nodal Point
  • light that passes here goes straight and is not refracted
    2. Focal Point 1/Primary Focal Point
  • light leaving an object at this point is DIVERGENT and emerges PARALLEL from the lens
  • if object placed CLOSER than F1: divergence of incident rays GREATER than converging power of lens = light leaves lens DIVERGING
  • if object placed FARTHER than F1: divergence of incident rays LESS than converging power of lens = light leaves lens CONVERGING
    3. Focal Point 2/Secondary Focal Point
  • point of CONVERGENCE of PARALLEL light rays entering the lens
  • if incident light is DIVERGING, light will converge FARTHER than F2
  • if incident light is CONVERGING, light will converge CLOSER than F2
25
Q

What are cylindrical lenses?

A
  • Lenses cut from a glass CYLINDER
  • Focuses light to a LINE (FOCAL AXIS)
  • Has an AXIS: FLAT meridian with NO lens power (PLANO)
  • MAXIMUM POWER: the MOST CURVED meridian 90 degrees away from the axis
  • Corrects astigmatism
  • Can either be:
    1. Convex/Positive/Converging
    2. Concave/Negative/Diverging

Note: 2 equal cylinders at right angles = spherical lens

E.g.
Cylinder with axis 90 degrees:
- Cylinder oriented vertically (upright)
- Focal axis: vertical line at 90 degree meridian
- Power at 90 degrees: Plano (0 D)
- Power at 180 degrees: Maximum lens power

Cylinder with axis at 180 degrees:

  • Cylinder oriented horizontally
  • Focal axis: horizontal line at 180 degree meridian
  • Power at 90 degrees: Maximum lens power
  • Power at 180 degrees: Plano (0 D)
26
Q

What are the primary meridians of the cylinder lens?

A

Power Meridian

  • curved/steepest part of the lens
  • contains the correcting power of the lens
  • 90 degrees away from the axis.

Axis Meridian

  • flat part of the lens
  • contains zero power
  • denotes the orientation of the glass cylinder the lens was cut from
  • describes the orientation of the line where light is focused at
27
Q

What are sphero-cylindrical lenses/compound lenses/TORIC lenses?

A
  • Combination of a sphere and a cylinder
  • Lens cut from a glass torus (looks like a foot ball)
  • Used to correct COMPOUND astigmatism where the cornea has TWO PRINCIPAL MERIDIANS of power acting 90 degrees to each other (neither is plano)
  • TWO completely independent radius of curvature
  • Represented by the Conoid of Sturm where difference in power between the two primary meridians causes light rays to focus on two different focal lines.
28
Q

What is the Conoid of Sturm?

A
  • Visual representation of how rays are refracted through the different powered meridians in a sphero-cylindrical lens
  • Forms two focal lines 90 degrees apart
  • Bundle of rays formed by an astigmatic optical system that changes in shape as it passes away from the cornea
  • Size depends on the difference of power of the two meridians: the larger the difference, the wider the conoid
  • Consists of:
    1. Primary Focal Line: convergence of rays from meridian with MOST power focusing CLOSER to the cornea
    2. Secondary Focal Line: formed by meridian with LEAST power; PERPENDICULAR to the primary and FARTHER from the cornea
    3. Interval of Sturm: area between the two focal lines; images formed here are blurred circles of different sizes
    4. Circle of Least Confusion
  • a circular area with best overall focus
  • located at the midpoint between the two focal lines
  • should fall onto the retina to provide best image quality
29
Q

What is astigmatism and what are the different kinds?

A

Astigmatism
- an asymmetry in the shape or curvature of the cornea or lens that prevents light from focusing properly on the retina

  1. Simple Myopic
    - one focal line falls ON THE RETINA, the other IN FRONT
  2. Simple Hyperopic
    - one focal line falls ON THE RETINA, the other BEHIND
  3. Compound Myopic
    - both focal lines fall IN FRONT of the retina
  4. Compound Hyperopic
    - both focal lines fall BEHIND the retina
  5. Mixed
    - one focal line falls IN FRONT, the other BEHIND
30
Q

Represents the power of the lens acting in every meridian.

A

Power Cross/Cross Diagram

31
Q

Lens having the effect of two cylindrical lenses (one PLUS lens, the other MINUS lens) of equal strength placed with their axes perpendicular to each other.

A

Jackson Cross Cylinder

32
Q

Compare Spherical vs Cylindrical vs Toric/Sphero-Cylindrical Lenses.

A

Spherical

  • focus at a point
  • similar power on all meridian
  • corrects simple myopia/hyperopia

Cylindrical

  • focus at a line
  • (+) Axis: 0 power, describes orientation of focal line
  • (+) Power: meridian with maximum power 90 deg. from axis
  • corrects astigmatism
  • power in the other meridians is between max power and 0

Toric

  • focus is an area (circle of least confusion)
  • 2 prime meridians with independent radius of curvature and diff. powers 90 deg. from each other
  • corrects astigmatism
  • power in the other meridians is between powers of 2 prime meridians
33
Q

Reminders about lens system construction.

A
  1. Lenses are additive with respect to the signs.
  2. A toric lens can be constructed using a spherical + cylindrical lens or two cylindrical lenses.
  3. A toric system can be created using a PLUS cylinder or a MINUS cylinder and they can be interconverted into each other.
  4. Sphere power meridian = AXIS of cylinder (PLANO power)

Toric System using sphere and PLUS cylinder:

  • sphere power = LOWER powered meridian
  • e.g. +3D sph + 2D cyl x 180

Toric System using sphere and MINUS cylinder

  • more commonly used because more people are myopic than hyperopic (minus lens to diverge light back to retina)
  • sphere power = HIGHER powered meridian
  • higher meaning MORE positive or LESS negative
  • e.g. +5D sph + -2D x 90

Toric System using 2 cylinders

  • no sphere power
  • use two cylinders with different powers perpendicular to each other
34
Q

What are the steps in the transposition of lens from PLUS cyl to MINUS cyl to two cylinder systems?

A

PLUS to MINUS cyl or vice-versa:

  1. Add power of sph and cyl RESPECTING the signs
  2. Change sign of cyl
  3. Switch axis to perpendicular angle.

PLUS/MINUS cyl to 2 cylinder systems:

  1. Combine sph + cyl notation into the resultant lens system
  2. Convert to two cyl systems (Cyl Power 1 x Axis 1 + Cyl Power 2 x Axis 2)
35
Q

What is the spherical equivalent?

A
  • If you have a non-spherical lens system (cyl/toric) but a spherical lens should be used for the patient (contact lenses), this estimates the lens power closest to the power of the system.
  • Simply put: HALF the power of the lens system

To compute, either:

  1. Make resultant lens system cross diagram to get the power of each prime meridian. SE will be the power halfway between the two.
  2. Divide cyl power by 2 and add the half to the sphere power algebraically RESPECTING the signs.
36
Q

How to construct a ray diagram for a PLUS lens?

A
  1. Ray 1: draw an incident ray from the object passing through the center of the lens (NOT refracted)
  2. Ray 2: draw an incident ray passing through PRIMARY FOCAL POINT on the SAME side and emerging parallel from the lens
  3. Ray 3: draw an incident ray entering the lens parallel and passing through the SECONDARY FOCAL POINT on the OPPOSITE side

Intersection: Image is REAL, INVERTED, MAGNIFIED

37
Q

How to construct a ray diagram for a MINUS lens?

A
  1. Ray 1: draw an incident ray from the object passing through the center of the lens (NOT refracted)
  2. Ray 2: draw an incident ray directed to the PRIMARY FOCAL POINT at the OPPOSITE side but exiting parallel (then trace an imaginary line connecting to the parallel ray)
  3. Ray 3: draw an incident ray entering the lens parallel and exiting divergent (then trace an imaginary line extending from the divergent ray and passing through the SECONDARY FOCAL POINT at the SAME side

Intersection: Image is IMAGINARY, UPRIGHT and MINIFIED