Rectilinear propagation
When light travels through a homogeneous medium, it travels in a straight line. This is known as rectilinear propagation.
Reflection
Reflection is the rebounding of incident light waves at the boundary of a medium.
Law of reflection
θ1 = θ2
θ1 is the incident angle
θ2 is the reflected angle
Both are measured from the normal
Normal
The normal is a line drawn perpendicular to the boundary of a medium.
In general, images created by a mirror can be either _____ or _____.
real
virtual
Real image
An image is said to be real if the light actually converges at the position of the image.
Virtual image
An image is virtual if the light only appears to be coming from the position of the image but does not actually converge there.
One of the distinguishing features of real images is the ability of the image to be _____.
projected onto a screen
Plane mirror behavior
Parallel incident light rays remain parallel after reflection from a plane mirror; that is, plane mirrors—being flat reflective surfaces—cause neither convergence nor divergence of reflected light rays.
Plane mirrors always create _____ images
virtual
How can you tell that a mirror produces a virtual image?
Because the reflected light remains in front of the mirror but the image appears behind the mirror (i.e. light does not actually pass through the image's location)
Spherical mirrors come in two varieties: _____ and _____.
concave and convex
Spherical mirror
A spherical mirror can be considered a spherical cap or dome taken from a much larger spherically shaped mirror.
Concave
Having an outline or surface that curves inward like the interior of a circle or sphere. If we were to look from the inside of a sphere to its surface, we would see a concave surface.
Convex
Having an outline or surface curved like the exterior of a circle or sphere. If we were to look from outside the sphere, we would see a convex surface.
Concave mirrors are called _____ and convex mirrors are called _____.
converging mirrors
diverging mirrors
MNEMONIC: Concave is like looking _____.
into a cave
Parallel incident light rays to a concave mirror _____.
converge
Parallel incident light rays to a convex mirror _____.
diverge
Focal length
The focal length (f) is the distance between the focal point (F) and the mirror.
Equation for focal length of a spherical mirror
radius of curvature (r) is the distance between C and the mirror
Relationship between key variables in geometric optics
f is focal length
o is the distance between the object and the mirror
i is the distance between the image and the mirror
r is the radius of curvature
While it is not important which units of distance are used in this equation, it is important that all values used have the same units as each other.
Center of curvature
The center of curvature (C) would be the center of the spherically shaped mirror if it were a complete sphere.
Radius of curvature
The radius of curvature (r) distance between the center of curvature and the mirror.
Key variables in geometric optics (diagram)
Image distance
The distance between the image and the mirror
If the image has a _____, it is a real image, which implies that the image is _____ the mirror.
positive distance (i > 0)
in front of
If the image has a _____, it is virtual and thus located _____ the mirror.
negative distance (i < 0)
behind
Plane mirrors can be thought of as _____.
What is the consequence of this?
spherical mirrors with infinitely large focal distances
As such, for a plane mirror, r = f = ∞, and the equation becomes 1/o + 1/i = 0, or i = –o.
For a plane mirror, the virtual image is ...
... at a distance behind the mirror equal to the distance the object is in front of the mirror.
Magnification equation
The magnification gives the ratio of ...
... the size of the image to the size of the object.
Magnification
The magnification (m) is a dimensionless value that is the ratio of the image distance to the object distance.
A negative magnification signifies an _____ image.
inverted
A positive magnification signifies an _____ image.
upright
If |m| < 1, the image is _____ than the object.
smaller (reduced)
If |m| > 1, the image is _____ than the object.
larger (enlarged)
If |m| = 1, the image is _____ the object.
the same size as
Ray diagram
A ray diagram is a diagram that traces the path that light takes in order for a person to view a point on the image of an object.
For a concave mirror, a ray that strikes the mirror parallel to the axis is reflected back _____.
through the focal point
Axis of a mirror
The normal passing through the center of the mirror
For a concave mirror, a ray that passes through the focal point before reaching the mirror is reflected back _____.
parallel to the axis
For a concave mirror, a ray that strikes the mirror at the point of intersection with the axis is reflected back _____.
with the same angle measured from the normal
Any time an object is at the focal point of a converging mirror or lens, the reflected rays will be _____, and thus, the image will be _____.
parallel
at infinity
When an object is placed at a distance f away from a convergent mirror or lens, the image is _____.
at infinity/nonexistent
When an object is placed at a distance 2f away from a convergent mirror or lens, the image is _____.
real, inverted, and the same size as the object
When an object is placed at a distance >2f away from a convergent mirror or lens, the image is _____.
real, inverted, and reduced
When an object is placed at a distance between 2f and f away from a convergent mirror or lens, the image is _____.
real, inverted, and enlarged
When an object is placed at a distance <f away from a convergent mirror or lens, the image is _____.
virtual, upright, and enlarged
When an object is placed in front of a diverging mirror or lens, the image is _____.
virtual, upright, and reduced regardless of the distance to the mirror
When an object is placed in front of a plane mirror, the image is _____.
virtual, upright, and the same size as the object regardless of the distance to the mirror.
The focal length of converging mirrors will always be _____. The focal length of diverging mirrors will always be _____.
positive
negative
MNEMONIC: UV NO IR
Upright images are always virtual
No image is formed when the object is a focal length away
Inverted images are always real
Inverted images are always _____.
real
Upright images are always _____.
virtual
Mirror: When o is positive, ...
... the object is in front of the mirror.
Mirror: When o is negative, ...
... the object is behind the mirror.
Note: this situation is rarely tested on the MCAT
Mirror: When i is positive, ...
... the image is real.
Mirror: When i is negative, ...
... the image is virtual.
Mirror: When r is positive, ...
... the mirror is concave (converging).
Mirror: When r is negative, ...
... the mirror is convex (diverging).
Mirror: When f is positive, ...
... the mirror is concave (converging).
Mirror: When f is negative, ...
... the mirror is convex (diverging).
Mirror: When m is positive, ...
... the image is upright (and virtual).
Mirror: When m is negative, ...
... the image is inverted (and real)
Mirror: When |m| > 1, ...
... the image is enlarged.
Mirror: When |m| < 1, ...
... the image is reduced.
Mirror: When |m| = 1, ...
... the image is the same size as the object.
For a concave mirror, a ray that is incident to the center of the mirror will _____.
be reflected back at same angle relative to normal.
Refraction
Refraction is the bending of light as it passes from one medium to another and changes speed.
The speed of light through any medium is always _____.
less than its speed through a vacuum
Index of refraction equation
c is the speed of light in a vacuum
ν is the speed of light in the medium
n is a dimensionless quantity called the index of refraction of the medium
The index of refraction of a vacuum is _____, by definition.
1
For all materials, the index of refraction will be _____.
greater than 1
For air, n is essentially _____.
equal to 1
The index of refraction of water is _____.
~1.33
Snell’s law
n1 sin θ1 = n2 sin θ2
n1 and θ1 refer to the medium from which the light is coming
n2 and θ2 refer to the medium into which the light is entering
Note that θ is measured with respect to the normal
When light enters a medium with a higher index of refraction (n2 > n1), it bends _____.
toward the normal
When light enters a medium with a smaller index of refraction (n2 < n1), the light will bend _____.
away from the normal
Critical angle
When light enters a medium with a smaller index of refraction, light bends away from the normal. As the incident angle is increased, the refracted angle also increases, and eventually, a special incident angle called the critical angle (θc) is reached, for which the refracted angle θ2 equals 90 degrees.
Critical angle equation
Total internal reflection
A phenomenon in which all the light incident on a boundary is reflected back into the original material and results from any angle of incidence greater than the critical angle, θc
Total internal reflection can only occur as the light moves from a medium with a _____ refractive index to a medium with a _____ one.
higher -> lower
When working with lenses, there are _____ that affect the light path.
two surfaces
On the MCAT, lenses generally have _____.
negligible thickness
Because light can travel from either side of a lens, a lens has _____.
two focal points
For thin spherical lenses, the focal lengths are _____.
equal
Relation between focal length, object distance, and image distance for lenses
Magnification of lenses
Lensmaker’s equation
n is the index of refraction of the lens material
r1 is the radius of curvature of the first lens surface
r2 is the radius of curvature of the second lens surface
A converging lens is always _____ at the center.
thicker
A diverging lens is always _____ at the center.
thinner
Lensmaker’s equation (use)
For lenses where the thickness cannot be neglected, the focal length is related to the curvature of the lens surfaces and the index of refraction of the lens by the lensmaker’s equation.
Diverging lenses are _____.
concave
Converging lenses are _____.
convex
What are the "lenses" of the eye?
The cornea acts as the primary source of refractive power because the change in refractive index from air is so significant.
Then, light is passed through an adaptive lens (the lens) that can change its focal length before reaching the vitreous humor.
It is further diffused through layers of retinal tissue to reach the rods and cones. At this stage, the image has been focused and minimized significantly, but is still relatively blurry. Our nervous system processes the remaining errors to provide a crisp view of the world.
A ray entering a lens parallel to the axis refracts _____.
through focal point of front face of the lens
A ray entering a lens through or toward the focal point before reaching the lens refracts _____.
parallel to the axis
A ray entering through the center of a lens ...
... continues straight through with no refraction.
Lens: A positive o means ...
Object is on same side of lens as light source
Lens: A negative o means ...
Object is on opposite side of lens from light source (extremely rare)
Lens: A positive i means ...
Image is on opposite side of lens from light source (real)
Lens: A negative i means ...
Image is on same side of lens as light source (virtual)
Lens: A positive r means ...
Lens is convex (converging)
Lens: A negative r means ...
Lens is concave (diverging)
Lens: A positive f means ...
Lens is convex (converging)
Lens: A negative f means ...
Lens is concave (diverging)
Lens: A positive m means ...
Image is upright (erect)
Lens: A negative m means ...
Image is inverted
The real side of a mirror is ...
... in front of the mirror.
The real side of a lens is ...
... the opposite side of the lens from the original light source.
The virtual side of a mirror is ...
... behind the mirror.
The virtual side of a lens is ...
... the same side of the lens as the original light source.
Lens: When |m| > 1, ...
... the image is enlarged.
Lens: When |m| < 1, ...
... the image is reduced.
Lens: When |m| = 1, ...
... the image is the same size as the object.
For both mirrors and lenses, _____ have positive focal lengths and radii of curvature, and _____ have negative focal lengths and radii of curvature.
converging species
diverging species
For a thin lens where thickness is negligible, the sign of the focal length and radius of curvature are given based on _____.
the first surface the light passes through
Lens power equation
f is the focal length
People who are nearsighted need _____, while people who are farsighted need _____.
diverging lenses
converging lenses
Lens power (P) is measured in _____.
diopters
The medical term for farsightedness is _____. This condition is treated with _____ lenses.
hyperopia
converging
The medical term for nearsightedness is _____. This condition is treated with _____ lenses.
myopia
diverging
In hyperopia, the focal point of the lens is _____ the retina.
behind
too little
In myopia, the focal point of the lens is _____ the retina.
in front of
too much
Focal length of a series of lenses in contact equation
Power of multiple lenses in contact equation
P = P1 + P2 + P3 + ··· + Pn
The eye has an optical power of around _____.
60 diopters
Even at its worst, the human eye can maintain its optical power at about _____ of its maximum.
87%
The cornea is a _____ lens.
converging
A good example of lenses in contact is a _____.
corrective contact lens
Magnification of multiple lenses not in contact equation.
m = m1 × m2 × m3 × ··· × mn
For lenses not in contact, the image of one lens becomes ...
... the object of another lens.
Spherical aberration
Spherical aberration is a blurring of the periphery of an image as a result of inadequate reflection of parallel beams at the edge of a mirror or inadequate refraction of parallel beams at the edge of a lens.
What is the result of spherical aberration?
This creates an area of multiple images with very slightly different image distances at the edge of the image, which appears blurry. (i.e. images are blurry at the edges)
Spherical mirrors/lenses are imperfect (spherical aberration), but _____ mirrors/lenses are essentially perfect.
parabolic
Chromatic aberration, discussed below, is predominantly seen in _____ lenses.
spherical
The speed of light in a vacuum is _____ for all wavelengths of light.
When light travels through a medium, different wavelengths travel at _____.
the same
different speeds
The index of refraction itself _____ with wavelength.
varies
Dispersion (light)
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Different wavelengths of light are refracted at different angles due to different refractive indeces, thus spreading the wavelengths apart.
Light at higher frequencies will travel _____ through materials than light of lower frequencies.
slower
In the visible light spectrum, red light _____ through mediums and gets refracted _____.
travels the fastest
the least
In the visible light spectrum, violet light _____ through mediums and gets refracted _____.
travels the slowest
the most
What changes and what stays the same when light enters a different medium
Wavelength and velocity change, but frequency (and thus, hue) stays the same
Chromatic aberration
A failure of a lens to focus all colors to the same point due to dispersion.
What is the result of chromatic aberration?
Chromatic aberration causes significant splitting of white light, which results in a rainbow halo around the edges of images.