Chapter 8: Light and Optics Flashcards
Electromagnetic Waves:
transverse waves that consists of an oscillating electric field and an oscillating magnetic field
the two fields are perpendicular to each other and to the direction of propagation of the wave
Electromagnetic Spectrum:
lowest to highest
radio waves, microwaves, infarered, visible light, ultraviolet, x-rays, γ-rays (gamma rays)
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Visible Spectrum wavelengths:
400-700nm
ROYGBIV
Red = 700nm
V = 380nm
speed of light value:
c = 3.00 x 108 m/s
How is color expressed?
(ex. white)
Light that contains all the colors in equal intensity is white
Ex: an object that appears red is one that absorbs all colors of light except red
Rectilinear propagation:
when light travels through a homogenous medium and travels in a straight line
Reflection:
- definition
- light waves that are reflected…
- rebounding of incident light waves at the boundary of a medium
- Light waves that are reflected are not absorbed into the second medium, they bounce off the boundary and travel back through the first medium
Law of Reflection:
Law of reflection: Θ1 = Θ2
*Θ1 = incident angle Θ2 = reflected angle*
Both are measured from the normal: a line drawn perpendicular to the boundary of a medium
All angles are measured from the medium
Plane Mirrors - Images:
- real images
- virtual images
Real: if the light actually converges at the position of the image - Image can be projected on a screen
Virtual: only appears to be coming from the position of the image but does not actual converge there
Plane Mirrors:
- what are they
- what they don’t cause the light to do
- type of images they always create
- how does this image appear
1. Plane mirrors: flat reflective surfaces
- Do not cause convergence or divergence of light rays
- Always create virtual, upright images that are the same size as the object
- Image appears to be the same distance behind the mirror as the object is in front of it
Center of Curvature (c):
a point on the optical axis located at a distance equal to the radius of curvature r from the vertex of the mirror
Center of curvature would be the center of the spherically-shaped mirror if it were a complete sphere
Spherical Mirrors - Concave surface:
- where center of curvature and radius of curvature are located
- diverging or converging?
- Center of curvature and the radius of curvature are located in front of the mirror
- Converging mirrors
Spherical Mirrors - Convex surface:
- where center of curvature and radius of curvature are located
- diverging or converging?
- Center of curvature and the radius of curvature are behind the mirror
- Diverging mirrors
Focal length (f):
- what it is
- for all spherical mirrors
- distance between the focal point (F) and the mirror
- For all spherical mirrors f = r/2, where the radius of curvature r is the distance between C and the mirror
o + i
(definitions)
o: distance between the object and the mirror
i: distance between the image and the mirror
Relationship between f, o, i and r
Image Distance:
- if the image has a positive distance (i > 0)
- if the image has a negative distance (i < 0)
- If the image has a positive distance (i > 0) it is a real image - Implies that the image is in front of the mirror
- If the image has a negative distance (i < 0) it is virtual - Image is located behind the mirror
Magnification (m):
- what it is
- equation
- dimensionless value that is the ratio of the image distance to the object distance
Give ratio of the size of the image to the size of the object
Values of Magnification:
- negative magnification
- positive magnification
- |m| > 1
- |m| < 1
- |m| = 1
- Negative magnification: inverted image
- Positive magnification: upright image
- If |m| < 1 the image is smaller than the object (reduced)
- If |m| > 1 the image is larger than the object (enlarged)
- If |m| = 1 the image is the same size as the object
Ray Diagram for a Concave Mirror:
- a ray that strikes the mirror parallel to the axis
- a ray that passes through the focal point before reaching the mirror
- a ray that strikes the mirror at the point of intersection with the axis
4. any time an object is at the focal point of a converging mirror
- A ray that strikes the mirror parallel to the axis is reflected back through the focal point (green lines)
- A ray that passes through the focal point before reaching the mirror is reflected back parallel to the axis (red lines)
- 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 (blue lines)
- Any time an object is at the focal point of a converging mirror, the reflected rays will be parallel and thus, the image will be at infinity
Ray Diagram for Concave Mirror:
Object is placed before F
diagram + image produced
Image produced:
real
inverted
magnified
Ray Diagram for Concave Mirror:
Object is placed at F
diagram + image produced
No image because the reflected light rays are parallel to each other
i = infinity
Ray Diagram for Concave Mirror:
Object is placed between F and the mirror
diagram + image produced
image produced:
Virtual
Upright
Magnified
A single diverging mirror:
- forms what kind of image
- does it depend on position
- what example to think about
- virtual, upright, and reduced image
- regardless of the position of the object
* The further away the object, the smaller the image will be* - Ex: convenience store security mirror
Sign Conventions for Mirrors:
Symbol (o, i, r, f, m)
Positive
Negative
o
- Positive: Object is in front of the mirror
- Negative: Object is behind mirror (very rare)
i
- Positive: Image is in front of mirror (real)
- Negative: Image is behind mirror (virtual)
r
- Positive: Mirror is concave (converging)
- Negative: Mirror is convex (diverging)
f
- Positive: Mirror is concave (converging)
- Negative: Mirror is convex (diverging)
m
- Positive: Image is upright (erect)
- Negative: Image is inverted
Focal Length of converging and diverging mirrors:
(inverted vs. upright images)
The focal length of converging mirrors (and converging lenses) will always be positive.
The focal length of diverging mirrors (and diverging lenses) will always be negative.
Inverted images are always real
Upright images are always virtual
Refraction:
- what it is
- the speed of light thru a medium vs. a vacuum
- 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 and variables
- index of refraction for a vaccuum vs. air
c = speed of light in a vacuum v = speed of light in the medium n = index of refraction
Index of refraction for a vacuum = 1
For air, n is essentially 1
Snell’s Law as refracted rays of light pass from one medium to another:
- equation
- when light enters a medium with a higher index of refraction
- when light enters a medium with a lower index of refraction
- n1 sin Θ1 = n2 sin Θ2
- When light enters a medium with a higher index of refraction (n2 > n1), it bends toward the normal (sinΘ1 < sinΘ2 ; therefore Θ2 < Θ1)
- The opposite is true when light enters a medium with a smaller index of refraction, the light will bend away from the normal
Total Internal Reflection - Critical Angle:
- what it is
- equation
when the refracted angle equals 90 degrees
Total internal reflection:
- what it is
- results with what?
3. major thing to remember
- phenomenon in which all the light incident on a boundary is reflected back into the original material
- Results with any angle of incidence greater than the critical angle (when the refracted angle equals 90 degrees)
- Total internal reflection occurs as the light moves from a medium with a higher refractive index to a medium with a lower one
Thin Spherical Lens:
- focal points
Because light can travel from either side of the lens, a lens has two focal points, with one on each side
Can be measured in either direction from the center
Focal lengths are equal for this lens
Real lenses:
- what they are
- focal length relationship + equation
- Lenses in which thickness cannot be neglected
- Focal length is related to the curvature of the lens surfaces and the index of refraction of the lens by the lensmaker’s equation:
Sign Conventions for Lenses:
Symbol (o, i, r, f, m)
Positive
Negative
o
- Positive: Object is on same side of lens as light source
- Negative: Object is on opposite side of lens from light source (extremely rare)
i
- Positive: Image is on opposite side of lens from light source (real)
- Negative: Image is on same side of lens as light source (virtual)
r
- Positive: Lens is convex (converging)
- Negative: Lens is concave (diverging)
f
- Positive: Lens is convex (converging)
- Negative: Lens is concave (diverging)
m
- Positive: Image is upright (erect)
- Negative: Image is inverted
Power:
- measured in what
- equation
- converging versus diverging lens
- nearsighted vs. farsighted
- Measured in diopters
- P is positive for a converging lens and negative for a diverging lens
- Nearsighted = diverging lenses
Farsighted = converging lenses
Multiple Lens Systems:
- definition
- focal length relationship
- power relationship
- magnification relationship
- Lenses in contact are a series of lenses with negligible distances between them
- Have a equivalent focal length: see image
- Equivalent power: P = P1 + P2 + P3 + ··· + Pn
- Magnification for the system: m = m1 × m2 × m3 × ··· × mn
Abberations:
errors in lenses
Spherical Aberrations:
blurring of the periphery of an image as a result of inadequate reflection of parallel beams at the edge of a mirror or inadequate reflection of parallel beans at the edge of a lens
Creates an area of multiple images with very slightly different image distances at the edge of the image, which appears blurry
Dispersion:
when various wavelengths of light separate from each other
Ex: splitting of white light into its component colors using a prism
Chromatic Aberration:
dispersive effect within a spherical lens
Phenomenon is correct in glasses and lenses with special coatings
Diffraction:
refers to the spreading of light as it passes through a narrow opening or around an obstacle
Slit lens and double-slit systems
Diffraction - Single Slit:
- what happens
- as the slit is narrowed
- When light passes through a narrow opening (an opening that is on the order of light wavelengths), the light waves spread out (diffract)
- As the slit is narrowed, the light spreads out more
Diffraction - Slit-Lens System:
- what happens if a lens is placed between a narrow slit and a screen
- central fringe vs. bright fringes
- as slit becomes narrower
- If a lens is placed between a narrow slit and a screen, a pattern is observed that looks like a bright central fringe with alternating dark and bright fringes on each side
- The central fringe (max) is twice as wide as the bright fringes on the sides
- As the slit becomes narrower, the central maximum becomes wider
Slit-Lens System:
- location of the dark fringes (minima) given by what formula (+ variables)
Location of the dark fringes (minima) is given by the formula:
a sin θ = nλ
*a = width of slit Θ = angle between the line drawn from the center of lens to the dark fringe and the axis of the lens n = integer indicating the number of the fringe λ = wavelength of the incident wave*
Interference:
when waves interact with each other and the displacement of the waves add together
Young’s double-slit experiment:
When monochromatic light (light of only one wavelength) passes through the slits, an interference pattern is observed on a screen placed behind the slits
Regions of constructive interference between the two lights appear as bright fringes (maxima)
Regions where the light waves interfere destructively are where dark fringes (minima) appear
Multiple Slits - the positions of dark fringes:
- equation + variables
- relationship between bright and dark fringes
*d = distance between the two slits Θ = angle between the line drawn from the midpoint between the two slits to the dark fringe and the normal N = integer indicating the number of the fringe λ = wavelength of the incident wave*
2. Bright fringes are halfway between dark fringes
Diffraction gratings:
consist of multiple slits arranged in patterns
Create color patterns like a prism as the different wavelengths interfere in characteristic patterns
Ex: on a CD or DVD
X-ray Diffraction
Uses the bending of light rays to create a model of molecules
Dark and light fringes take on a complex two dimensional image
Plane-polarized (or linearly polarized) light:
light in which the electric fields of all the waves are oriented in the same direction
i.e: their electric field vectors are a parallel
Applications of Plane Polarized Light:
Applications - stereoisomers
The optical activity of a compound (due to chiral centers), causes plane-polarized light to rotate clockwise or counterclockwise by a given number of degrees relative to its concentration (specific rotation)
Enantiomers (nonsuperimposable mirror images) will have opposite specific rotations
Electric Fields of Unpolarized light vs. Polarized light:
The electric fields of unpolarized light waves exist in all three dimensions: the direction of the wave’s propagation is surrounded by electric fields in every plane perpendicular to that direction
Polarizing light limits the electric field’s oscillation to only two dimensions
Circular Polarization:
- occurence
- results from what
- amplitude + direction
Rarely seen naturally
Results from the interaction of light with certain pigments or highly specialized filters
Uniform amplitude but continuously changing direction
