Ch 8 - Light and Optics Flashcards
electromagnetic spectrum from lowest energy to highest energy
radio waves (wavelength range from 10^9 - 1 m), microwaves (1 m - 1 mm), infrared (1 mm - 700 nm), visible light (700 nm - 400 nm), ultraviolet (400 - 50 nm), x-rays (50 - 10^-2 nm), gamma rays (less than 10^-2 nm)
electromagnetic waves
transverse waves - oscillating electric and magnetic field vectors are perpendicular to the direction of propagation and each field is perpendicular to each other.
common units of wavelength
mm (10^-3 m), fancy um (mu) (10^-6 m), nm (10^9 m) and A with a circle at the point (angstrom, 10^-10 m)
visible spectrum from lowest to highest energy
Red, orange, yellow, green, blue, violet (roy g bv)
speed of light
EM waves travel this fast in a vacuum and in air: c = 3.00 x 10^8 m/s
equation for speed of light
c = f x wavelength; f = frequency; c = speed of light in air and vacuum
approximate wavelength boundaries of the visible spectrum
400-700 nm
blackbody
ideal absorber of all wavelengths of light, which would appear completely back if it were at a lower temp than its surroundings
rectilinear propagation
concept that light travelling through a homogenous medium will travel in a straight line
reflection
rebounding of incident light waves at the boundary of a medium
law of reflection
theta sub 1 = theta sub 2 (angles of reflection); theta sub 1 = angle of incident and theta sub 2 = reflected angle
normal (in reference to reflection)
a line drawn perpendicular to the boundary of a medium; all angles in optics are measured from the normal, not the surface of the medium
real image
image in which the light actually converges at the position of the image; this image can be projected onto a screen
virtual image
image in which the light only appears to be coming from the position of the image but does not actually converge there
plane mirrors
flat reflective surfaces that cause neither convergence nor divergence of reflected light rays; because light does not converge at all, these always created virtual images because reflected light remains in front of the mirror but the image appears behind the mirror
spherical mirrors
come in two varieties: concave and convex and have associated center of curvature (C) and radius of curvature (r)
center of curvature
point on the optical axis located at a distance equal to the radius of curvature from the vertex of the mirror; the center of the spherically shaped mirror if it were a complete sphere
concave mirror
also called converging mirrors; edges coming towards you; center of curvature and radius of curvature are located in front of the mirror
convex
also called diverging mirrors; surface coming towards you; edges away; center of curvature and radius of curvature are behind the mirror
focal length (f) of mirror
distance between focal point (F) and mirror
focal length for spherical mirror
f = r/2 where radius of curvature (r) is distance between C (center of curvature) and the mirror
relationship between four important distances of spherical mirrors
1/f = 1/o + 1/i = 2/r; where f = focal length, o = distance between object and mirror, i = distance between image and mirror, r = radius of curvature
image distance greater than 0
real image which implies that the image is in front of the mirror
image distance less than 0
virtual image; image is behind the mirror
magnification (m)
dimensionless value that is the ratio of the image distance to the object distance (m = -i/o); also gives ratio of the size of the image to the size of the object
inverted image
negative magnification value
upright image
positive magnification value
what happens to image where |m| < 1
image is smaller than object
what happens to image if |m| > 1
image is larger than the object
what happens if image is |m| = 1
image is same size as object
ray diagram
gets approximations of where an image is using o, C, F, and I
axis
the normal passing through the center of the mirror
converging (concave mirror): if object is between focal point and mirror
image is virtual, upright and magnified
converging (concave mirror): if object is beyond focal point
image is real, inverted and magnified
converging (concave mirror): if object is placed at focal point
no image is produced. i = infinity
image produced by diverging mirror
virtual, upright and reduced only
when i is positive or negative
positive i indicates image is in front of mirror (real); negative indicates image is behind mirror (virtual)
when o is positive or negative
positive indicates object is in front of mirror; negative is very rare and indicates object is behind mirror
when r is positive or negative
positive radius indicates mirror is concave (converging); negative indicates mirror is diverging (convex)
when f is positive or negative
positive indicates mirror is concave (converging); negative indicates mirror is convex (diverging)
when m is positive or negative
positive indicates image is upright (erect); negative indicates image is inverted
refraction
bending of light as it passes from one medium to another and changes speed; speed is always less than through a vacuum
Snell’s Law
when light is in any medium besides a vacuum speed is less than c and is given by n = c/v; where c = speed of light in vacuum, v = speed of light in the medium, and n = dimensionless quantity called index of refraction of the medium
equation relating to Snell’s Law as light passes from one medium to another
n sub 1 sin theta sub 1 = n sub 2 sin theta sub 2; n sub 1 = index of refraction of medium from which the light is coming and theta sub 1 = angle of refraction in reference to the normal from this medium and sub 2 = same of medium to which light is going
critical angle
theta sub c; angle at which refracted angle (theta sub 2) = 90 degrees; refracted light ray passes along the interface between the two media
critical angle equation
theta sub c = sin^-1 ((n sub 2)/n sub 1);
total internal reflection
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 (theta sub c)
difference between lenses and mirrors
lenses refract light while mirrors reflect it; also lenses have two surfaces that affect the light path: from an object through the air into the glass lens (first surface); and through the glass until it reaches the other side, where again it travels out of the glass and into the air (second surface); two focal points and focal length can be measured in either direction from the center
thin spherical lens focal length
have one focal length because the two are the same to one side and the other
formulas for finding distance and magnification for thin spherical lenses
1/f = 1/o + 1/i = 2/r and m = -i/o. f = focal length, o = object distance, i = image distance, m = magnification
real lens focal length (lensmaker’s equation)
1/f = (n - 1) ((1/r sub 1) - (1/ r sub 2)); n = index of refraction for lens material; r sub 1 = radius of curvature for first lens surface; r sub 2 is for second lens surface
meaning when o is positive or negative for single lenses
positive means object is on same side of lens as light source; negative means object is on opposite side of lens (extremely rare)
meaning when i is positive or negative for single lenses
positive means image is on opposite side of lens from light source (real); negative means image is on same side as light source (virtual)
meaning when r is positive or negative for single lenses
positive means lens is convex (converging); negative means lens is concave (diverging)
meaning when f is positive or negative for single lenses
positive means lens is convex (converging); negative means lens is concave (diverging)
meaning when m is positive or negative for single lenses
positive means image is upright (erect); negative means image is inverted
Power of lens
measured in diopters: P = 1/f; where f = focal length and is in meters; P is positive for converging lens and negative for diverging
nearsighted people need
diverging lenses (nearsightedness is myopia)
farsighted people need
converging lenses (farsightedness is hyperopia)
focal length of multiple lenses in system
1/f = 1/f sub 1 + 1/f sub 2 + 1/f sub 3 …. etc
power of multiple lenses in system
P = P sub 1 + P sub 2 etc
magnification for multiple lens systems
m = m sub 1 x m sub 2 … etc
aberrations
specific types of errors found in mirrors and lenses
spherical aberration
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
dispersion
when various wavelengths of light separate from each other
chromatic aberration
dispersive effect within a spherical lens which causes a rainbow halo around images
Diffraction
refers to spreading out of light as it passes through a narrow opening or around an obstacle
location of dark fringes (minima) in diffraction
a sin theta = n x wavelength; a = width of the slit through which light is passing; theta = angle between line drawn from the center of the lens to the dark fringe and that axis of the lens; n = an integer indicating the number of the fringe; wavelength = incident wave
interference
when waves interact with each other this is the process of the displacement of the waves added together
positions of dark fringes (minima) on a screen
d sin theta = (n + (1/2)) x wavelength; d = distance between the two slits; theta = angle between the line drawn from the midpoint between the two slits to the dark fringe and the normal; n = integer indicating number of the fringe; wavelength is incident wave
Diffraction gratings
consist of multiple slits arranged in patters; can create colorful patterns similar to a prism as the different wavelengths interfere in characteristic patterns
light fringes
created from multiple slit systems; result from constructive and destructive interference between light rays
plane-polarized light
also called linearly polarized light; light in which electric fields of all the waves are oriented in the same direction (their electric field vectors are parallel)
