week 9 Flashcards
what is light?
- an electromagnetic wave
- a self-propagating combination of oscillating electric and magnetic fields
visible light ranges between
380 and 750 nm
what is refraction?
when a ray of light is transmitted obliquely through the boundary between two materials of unlike index of refraction, the ray bends
the absolute index of refraction of a material is defined as
n = speed of light in vacuum / speed of light in the material
or
n = c / v
what is the relative index of refraction of material 1 with respect to material 2
relative index = n1 / n2
- n1 and n2 are the absolute refractive indices of the 2 material
what happens when n2 > n1, and what happens when n2 < n1
- the ray bends toward the normal as it enters the second material
- the ray bends away from the normal
what 3 aspects lie on the same plane?
the incident ray, refracted ray, and the normal
what are the angles θi and θr called respectively?
angle of incidence, angle of refraction
what does Snell’s Law give?
the way in which a ray refracts at an interface between materials with indices of refraction (ni) and (nr)
what is the equation of Snell’s Law
n1 sinθ1 = n2 sinθ2
what is reflection?
when light hits the surface of almost any material, some of that light ‘bounces back’ off the surface
what does the law of reflection state?
the reflected light leaves the surface at the same angle that the incident light falls on
equation of the law of reflection
θi = θrfl
two ways reflection can be described
specular or diffuse
specular reflection
- when light hits a very flat, reflective surface, such as a mirror
- all light coming from a single direction is reflected in a single direction
diffuse reflection
when the surface is rougher, the light is reflected in a wide range of directions
what is total internal reflection?
the complete reflection of an incident light ray at a boundary, with no transmission
when does total internal reflection occur?
it occurs only for waves incident on a boundary with a medium where the reflective index is reduced
critical angle
n1 sinθc = n2 sin90 = n2
θc = sin^-1 n2 / n1
when the angle of incidence is larger than the critical angle
none of the wave is transmitted through the boundary, only reflection occurs
what is the requirement for materials to be transparent?
visible wavelengths of electromagnetic radiation must pass through without being absorbed
the refractive index is _____ on the shorter wavelength side and _____ on the longer wavelength side
higher, lower
what is dispersion? what are dispersive media?
- when the wave speed is depended on the frequency
- materials with this property are called dispersive media
converging (or positive) lenses are _____ at the center than at the rim, while diverging (or negative) lenses are _____ at the center
thicker, thinner
what is the focal point of a thin lens with spherical surfaces?
the point f where rays parallel to and near the center or optical axis are brought to a focus
focus is _____ for a converging lens and ______ for a diverging lens
real, virtual
what is the focal length (f)
the distance of the peripheral focus from the lens
all rays passing through the lens form an image a positive distance d2 to the right of the lens, which is given by the equation
1 / d1 + 1 / d2 = 1 / f
when is a real image formed at d2?
- when d1 > f
- which means that we will see the image at d2 if we place a screen (such as a piece of paper)
converging lenses form inverted real images of objects located where?
outside the principal focus
what occurs when the object is between the principal focus and the lens?
the image is virtual (on the same side of the lens as the object), erect, and enlarged
what parts of the eye are positive lenses?
the cornea and crystalline lens
because they need to form a real image on the retina
corrective lenses (eyeglasses) can have a positive focal length _____ or a negative focal length _____
presbyopia, myopia
the power of a lens is the _____, and is measured in _____
- the inverse of its focal length
- diopters (D)
the Lensmaker’s equation is
1 / f = (n - 1) ( 1/ r1 - 1/ r2)
when is the radius of a curvature (r) positive? when is it negative?
positive - when its center of curvature lies to the right of the surface
negative - when its center of curvature lies to the left of the surface
what shapes do lenses of positive focal lengths have?
- biconvex
- planoconvex (one side flat)
- positive meniscus
what shapes do lenses of negative focal lengths have?
- biconcave
- planoconcave
- negative meniscus
isolated cornea is a
a negative meniscus lens
the crystalline lens is a
an asymmetric biconvex lens
which images are inverted? which images are upright
real images are inverted
virtual images are upright
why is the cornea transparent?
because it is uniform in structure, avascular except in the extreme periphery, and relatively dehydrated
what is the cornea covered by?
a 7-10 µm thick layer of tears
(which smooths over optical irregularities and supplies the cornea with oxygen)
what is the average radius of curvature of the anterior surface of the cornea?
about 7.8 mm in the central region with a variation of about ±0.4 mm, and is flatter in the periphery
the pupil in the iris can vary from ___ to ___ in diameter
1.5 to 10 mm
what controls the diameter of the pupil?
an opposing pair of smooth muscles
where is the crystalline lens suspended? how thick is it and what is its diameter?
- it is suspended and rests on the posterior surface of the iris
- it is about 4mm thick and 9mm in diameter
what is the formation of an image on the retina determined by?
- the indices of refraction of each eye component that the light passes through
- the shapes of the surface of these elements in the eye
what performs two-thirds of the focusing and what performs the remaining one-third?
two-thirds: the cornea
one-third: the crystalline lens
describe the rod cells in the retina
- 120 million
- high sensitivity
- low spatial acuity (detection of shape)
- more numerous in the periphery
what is the sensitivity of rods? what is the diameter?
500 nm, 2µm
what two kinds of vision are rods responsible for?
night vision and peripheral vision
two reasons why visual acuity is decreased in the outer portions of the retina
- rods are far from the fovea
- many rods are connected to the same nerve fiber
describe the cone cells in the retina
- 6.5 million
- low sensitivity
- high spatial awareness
- concentrated in the fovea
what are the 3 types of cone cells and their respective spectral sensitivities?
- blue cones (445 nm)
- green cones (535 nm)
- red cones (670 nm)
when does absorption occur?
when the photons have energy in ranges that can be absorbed by the photosensitive molecules (rhodopsin) in these cells
only 50% of visible light reaches the retina, what are the reasons behind losses of light reaching the retina?
- reflection of light
- absorption
- scattering
what does transmission through the retina cause?
loss due to absorption and scattering within the retina before light hits the rods and cones
what is the reflected fraction at the air/cornea interface?
2%
most of the light from ___ to ___ nm is absorbed by the crystalline lens
300 to 400
what are the schematic models for the imaging of rays in the eye?
- Gullstrand exact eye
- Reduced eye
- Schematic eye 1
Gullstrand exact eye model
- the most complete model
- has six refractive surfaces
- the variation of the refractive index within the lens is incuded
Reduced eye model
- simplest model
- only one refractive interface at the cornea
- all distances are relative to the single refractive surface
Schematic eye 1
- the refractive index within the crystalline lens is uniform
- contains 4 interfaces, 5 refractive indices, and radii of the 4 surfaces
what is accommodation?
the ability to control the focal length of the crystalline lens
what controls the curvature of the crystalline lens surfaces and thus its focal length
the tension in the ligaments suspended in the crystalline lens
what happens when the tension in ligaments is at a maximum?
the crystalline lens flattens and the focal length is at a maximum
what will a flatter lens produce? what will a larger curvature of the crystalline lens surface produce?
- clear images of distant objects
- a shorter focal length, which produces clear images of nearby objects
lack of appropriate accommodation is called
presbyopia
reasons behind the loss of accommodation with age
- increase in crystalline lens Young’s modulus
- flattening of the lens
- decrease in the lens capsule Young’s modulus
hyperopia
- farsightedness (can see far)
- due to long focal length, causing the image to be focused behind the retina, making it difficult for the person to see close up
myopia
- shortsightedness (can see near)
- due to short focal length, causing the images of distant objects to be focused in front of the retina
a myopic eye is corrected with a _____ lens while a hyperopic eye is corrected with a _____ lens
concave, convex
the near point has a normal of ___, while the far point has a normal of ___
- 25 cm
- infinity
