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What is Optics
- Light physics
- Science that studies the behavior of light
What is Light
- EM radiation part of the EMS
- A very narrow band of the EMS to which the eye is specifically sensitive
- Energy composed of oscillating magnetic and electric fields emitted by vibrating charged particles.
- Has "wave" like properties
Properties of waves
- Wavelength- distance from a point on a wave to that point on the next wave.
- Frequency- number of waves in 1 second
- Speed- distance the wave will travel in a second
- Amplitude- distance from the centerline to the peak
- Velocity= wavelenth x frequency
Visible light ranges
- 380-800 nm
- The shorter the wavelength, the more energy it carries, the more likely to cause cellular damage
- UV- shortest seen wavelength
Studies the nature of light and its interaction with mater (related to the wave nature of light)
Studies how light is propagated, reflected, and refracted (related to the postulate that light travels in straight lines)
One packet of light energy. A quantum of light. A particle of light. The smallest amount of light possible.
Path taken by a photon of light from a single point on a light source. A hypothetical line extending from the origin or focus of a wavefront that is perpendicular to all wavefronts emanating from the orgion or moving toward the focus of the wavelenth.
Any object that emits visible light
Sources of light
Luminois source that subtend small angles. It emits divergent light in all directions.
Source of light that subtends a finite angle. It produces overlapping groups of rays called beams.
Imaginary circles that eminate from a point source
The difference between an inner circle of a wavefront and an outer one is
time and distance
Fundamental Postulate of Geometrical Optics
- Rays are drawn in straight lines to represent rectangular propagation.
- All real objects omitt diverging rays from its source.
A section through a bundle of rays that contain a cheif ray.
A group of rays eminating from a point source
Rays don't overlap
Central ray. Ray that goes through the enter of the limiting aperature of the system.
A group of rays eminating from an extended source
Speed of Light
- Light travels slower in air then in a vaccuum.
- The velocity of visible light changes as light changes the medium in which it is travelling.
- 3 x 10 ^8 m/s
Index of Refraction
- Ratio that compares the speed of light in a vacuum to the speed of light as it moves through the material.
- n= speed of light in a vaccuum/ speed of light in the material
What happens to a wavefront as it gets farther from it's source?
The wavefronts become parallel to eachother
Light travels in straight lines in a homogenous medium.
Pinhole Camera Provides verification
Law of Rectilinear Propagation of Light
The manifestation of rectangular propagation of light
Sharp shadows produced by point sources
Region of partial shadow
The lines that spread apart as if originating from a point. They are said to have negative vergence.
Are lines that come together to meet at a point, then diverge again as they continue their path. They are said to have positive vergence.
The light that is reflected by an object results in color vision
An object appears to be black if it absorbs all the wavelengths, and reflects little or no light.
Appears to be white if it reflects all of the wavelenths
The bending or change in direction of light when it goes from one transparent material to another transparent materil of a different optical density.
Factors affecting Refraction
- The material itself (optical density)
- The obliquity of the incident light ray (perpendicular rays slow down)
- The wavelength of the incident light (different freq=different speeds)
When a ray of light is reflected from a surface, and angle of reflection will equal the angle of incidence.
Law of reflection
1st Law of Refraction
Ray of light striking an isotropic transparent surface normal (perpendicular) to the surface will not be bent, but the speed of light will be changed because of the change in optical density of the material.
2nd Law of Refraction
- A Ray of light striking a surface obliquely going from an isotropic media of lower optical density (fater, n lower), to an isotropic media of greater optical density (slower, n higher) will be bent toward the normal.
- lesser to greater= bent towards the normal
3rd Law of Refraction
- Ray of light striking a surface obliquely going from a isotropic media of greater optical density to a isotropic media or lesser optical density will be bent away from the normal.
- greater to lesser=bent away from the normal
The angle beween the light ray and the normal to the surface between the two materials
Angle of incidence
Angle at which the ray emerges into the second material
angle of refraction
The angle between the path of the refracted ray and the path the ray it would have taken if it had not been bent
Angle of deviation
Angle of incidence formula
<i = <d + <r
- When a ray of light travels from one material, the incident material, to another material, the refracting material, the direction will be changed according to
- ni(sini) = nr(sinr)
- ni= index of the incident material (first)
- nr= index of the refracting material
- i= angle of incidence
- r= angle of refraction
When light travels from a more dense material (n is higher) to a less dense material at just the right oblique angle, it is possible for the ray to emerge parallel to the surface of the refracting material.
The angle of incidence that results in the angle of refraction being 90˚
CA = sin-1 (nr/ni)
If the angle of incidence on light rays traveling from an optical medium of higher index of refraction to a medium of lower index, the rays will be refracted into the first medium,
Total Internal Reflection
Curvature of a sphere (C) is = to what?
The reciprocal of the radius of the sphere (1/l)
Quantitive measure of the degree of convergence or divergence of light in an optical medium at a particular position
D = 1/m
An arrangement of optical components that changes the vergence or direction of incident light causing the possible formation of an image
Objects are always condidered real when they emit ________ light
Images are always considered to be real when they are formed by _______ rays of light
Image formed by diverging rays of light
- If it is diverging- it is an optically real object
- If it is converging- then its an optically virtual object
- If converging- the image is optically real image
- If diverging- the image is an optically virtual image
Points related on either side of an optial system. Both can be on the same side of a system.
Ex- a real object forming a virtual image
The principle of reversibility
The rays representing the path of light through a system if reversed, will follow the origional path.
All points, rays, or ray extensions associated with light incident on an optical system
All points, rays, or ray extensions associated with light leaving an optical system.
If n'>n, the refracted ray is bent:
Toward the normal (r<i)
If n'<n, the refracted ray is bent
away from the normal (r>i)
Image distance formula l'
l' = tani/tanr (l)
Other formulas needed to solve image distance problems
- Snells law
When viewing an object immersed in another medium, what happens? What is this?
- The image of the object will be displaced (appear) in another location.
- Apparent Depth
By using the proof of congruency we can show what?
Tha the object and image with a plane mirror are of equal size as well as equidistant from the mirror.
Field of view formula
Summary of imagery with a plane mirror
- 1. The law of reflecton states that the angles of incidence and reflection are equal in size.
- 2. The image from a plane mirror is virtual, and located a distance behind the mirror equal to the distance that the object is in front of the mirror.
- 3. The image and object are of equal size and the image is erect (but reverted).
- image distance / object distance
Parallel plates summary:
- 1. A ray incident on a parallel plate will be refeacted in the opposite directions at each surface so that there is no change in direction of the ray.
- 2. However, the ray is displaced by an amount that is dependent on the initial angle of incidence (i), and the thickness (d) of the plate, as well as the refractive index (n) of the plate.
Displacement (e) formula
e= dsin∂ /cos r
- use snells law to get r
- use i=∂ = r1 to get ∂
- then plug it in to get e
Formed by two flat surfaces at an angle to one another
Prisms have no what?
Refracting power- it deviates light through it but does not change its vergence.
What happens at the apex
The image is displaced towards the apex
What happens towards the base
The rays bend toward the base
Light passing through a prism undergoes refraction where?
At both surfaces and exits refracted (deviated) toward the base.
What three things occur when light passes through a prism?
- Displacement of image
The Breaking up of white light into its component or spectral colors:
The refraction phenomenon
The angle of deviation formed after the ray of light has been refracted by both surfaces
- Deviating Angle
- Also known as apical angle
How to find the apical angle sigma
sigma = <a(n-1)
Only accurate for small prisms. The bigger the angle, the less accurate the formula.
Prism Diaptor formula
P= displacement in centimeters / displacement in meters
Single Spherical Refracting Interfaces
A single spherical surface between two optical media
Flat edge test
- If it is convex- put a (+) sign in front of it
- concave- always (-)
Dioptric power of the spherical interface- surface power
Surface power equation
distance from the surface to the focal point
the axial object point that results in plane waves leaving the interface, or the object point conjugate to optical infinity
Primary focal length
Primary focal length formula
f1 = - (n/P)
The axial image point that results when plane waves are incident on the interface, or the image point conjugate to optical infinity
Secondary focal length
Secondary focal length formula
f2 = n'/P
Paraxial Image Equation (need to find l' normally)
- (n'/l') = (n/l) + ((n'-n)/r)
- L'= L + P
- L' = n'/l'
- L = n/l
- P= (n'-n)/r
the ratio between the size of the image to that of the object
Lateral magnification formula
Y = (y'/y) = L/L'
When you need to solve for y or y' use:
(y'/y) = (n/l)(l'/n')
will also need the paraxial image equation to find the l's
A spherical lens consists of what?
Two optical surfaces separated by a transparent optical medium of higher refractive index than the surrounding medium.
A convex (+) surface will cause light to what?
Become more convergent and less divergent
A concave (-) surface will cause light to do what?
Become more divergent or less convergent
Charistics of a Plano Surface
- Flat surface
- Does not change the vergence of incident light
- Surface with infinitely large radius of curvature
- Plano- Pl
Convex Spherical Surface Characteristics
- Surface bulges
- It converges plane incident wavefronts
- Surface has plus power
Concave Spherical Surface Characteristics
- Surface is hallow
- It diverges plane incident wavefronts
- Surface has minus power
The surface that first interacts with light
The front surface
3 lens forms
- bi, plano, or meniscus
When a lens has a converging surface and a diverging surface the lens is called:
Meniscus or "Bent"
When a lens is not "bent" it is considered a "flat" lens
Bi-convex and bi-concave lenses
the image from one optical element in a series is the object for the next optical element:
conjugate points in a lens
The axial point that all off axis undeviated rays are incident to
1st nodal point
The axial point that all undeviated rays emerge from
2nd nodal point
The point where undeviated rays cross the optic axis
An imaginary line connecting the centers of curvature of the two surfaces of the lens.
The distance from the surface to a chord of the cross section circle
Sagittal depth (sag) (s)
The distance from the surface of the sphere to the center
Radius of curvature (r)
The location of the center of the sphere
Center of curvature (C)
The reciprocal of the radius in meters. The unit is in reciprocal meters (m-1).
A device that measures spherical surfaces by measuring the sag.
There are three fixed legs spaced equally around the circumference of a circle and a central leg that can be raised and lowered by a micrometer screw.
The radius of curvature is calculated from the previous equation where h is the distance from one central leg to one of the fixed legs.
r = h^2/2s
A device that measures the cuvature of one meridian of the surface by measuring the sag.
There are two fixed legs spaced equally from the central leg is raised and lowered by spring action.
Surface Power Calculation
F = n-1/r = R(n-1)
Lens clock calibration formula
Ftrue/ntrue-1 = Fclock/nclock-1
Refractive Components (5)
- Tear layer
- -Each component accounts for the overall refractive power of the eye.
- Anterior lipid layer
- Middle Aqueous layer
- Posterior Mucoid layer
- Bowman's layer
- Descernet's layer
- Anterior Lens Capsule
- Anterior Lens Cortex
- Posterior Lens Cortex
- Posterior Capsule
Most relavent optical components of the eye
- Cornea- 2/3 the overall power
- Lens- 1/3 the overall power
Controls the diameter of incoming beams of light
(Aperature Stop of the eye's optical system)
The relaxed eye has a total equivalent power of:
- - cornea is 2/3 of this - +40D
- -lens is other 1/3 - +20 D
Refractive indexes of the eye
- Cornea- 1.376
- Aqueus and Vitreus - 1.336
Variable focus power
- +10 D
- The change in equivalent power is accomplished by a change in the shape of the crystalline lens
When the object is closer, the ciliary muscle does what?
Contracts, and the lens increases focal power
The difference between the vergence powers incident on they eye from the far and near points is the
amplitude of accomidation
The physical limitation to the range of focal power of the eye determines what?
The farthest far point and the closest near point distances
The optic and visual axes:
- The fovea is the location of the image for the onject of interest fixated by the eye.
- The fovea subtends an angle of about 2 degrees
Why is there no true optical axis?
The optical system is not rotationally symmetrical
The empherical optic axis is determined by:
The direction of a small beam of light that minimizes the spread between the Purkinje images from the cornea and the lens.
What is the visual axis
The line passing through the fovea, nodal points, an the point of fixation.
The alpha angle
The angle between the visual and optical axes- is approx. five degrees.
- The iris is the aperature stop of the eye
- The image of the opening in the iris formed by the cornea is the enterance pupil.
- The size of the real pupil depends on several factors such as light level, drugs, psychological factors, and levels of accomodation.
- + accomidation = -pupil size
- The position and sixe of the entrance pupil is dependent on the focal power and location of the cornea.
- Changing the diameter of 2.. to 8mm only changes the retinal illumination by a fctor of 16.
- The change in the pupil size serves the function of optimal visual acuity.
Light and dark adaptation is a function of what?
The retina rather than the entrance pupil size
- The mean maximum and minimum pupil size decrease with age.
- 10- 3-7.5 mm
- 65- 2.5-5
The object point conjugate to the retina/fovea when accomidation is fully relaxed
The object point conjugate to retina/ fovea when accomidation is fully exerted
For whom, the far point is where they can see an object clear
myopes- its closer to the face
Emsley reduced eye
- no lens
- axial length- l= 22.222
- power = +60
- L' = L + F
- F= +60 (normally)
- F= n'-n / r
- l- n/L
- f' = -n/F
- n'= 1.333
- units in mm
the problem is the eye size
The problem is with the power of the eye
The object conjugate to the retina with the eye fully relaxed
With mirrors and lenses
- If L is negative = real object
- If L is positive = virtual object
- If L' is negative = virtual image
- If L' is positive = real image