Electromagnetic waves are transverse or longitudinal?

Transverse; they can also travel through a vacuum

Electromagnetic waves consist of what two oscillating fields?

an oscillating electric field and an oscillating magnetic field; the two fields are perpendicular to each other and to the direction of the propagation of the wave

The electromagnetic spectrum is:

the range of frequencies and wavelengths found in electromagnetic waves

The electromagnetic spectrum from lowest energy to highest energy:

radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays

Equation to determine the wavelength or frequency of light traveling in air or a vacuum:

c = fλ

where c is the speed of light and is equal to 3 X 10^{8};

units = m/s

1 angstrom =

1 X 10^{-10}

Electromagnetic waves vary in frequency and wavelength, but in a vacuum, they all travel at the same speed, which is:

the speed of light (3 X 10^{8} m/s)

The visible spectrum ranges from what wavelengths?

380nm (violet) to 760nm (red)

The order of the colors in the visible spectrum:

ROY-G BIV

red (760nm), orange, yellow, green, blue, indigo, violet (380nm)

Rectilinear propagation:

when light travels in a straight line through a single homogenous medium

Theory of geometrical optics describes:

the behavior of light at the boundary of a medium or interface between two media

Reflection is:

the rebounding of incident light waves at the boundary of a medium

Law of Reflection equation:

θ_{1} = θ_{2}

where θ_{1} is the incident angle and θ_{2} is the reflected angle

the angles are always measured from normal (a line perpendicular to the surface of the medium)

An image is real if:

the light converges at the position of the image

An image is virtual if:

the light appears to be coming from the position of the image, but does not actually converge there

Plane mirrors always create what kinds of images?

virtual, upright images the same size as the object since the light does not converge at all

The two types of spherical mirrors:

concave and convex; they both have centers and radii of curvature as well as focal points

Concave mirrors:

converging systems and can produce real, inverted images or virtual, upright images, depending on the placement of the object relative to focus

Convex mirrors:

diverging systems and will only produce virtual, upright images

The focal point of converging mirrors and converging lenses will always be:

positive

The focal point of diverging mirrors and diverging lenses will always be:

negative

Equation to determine the object or image distance from a mirror, focal length, or radius of curvature:

^{1}/_{o }+ ^{1}/_{i} =^{ 1}/_{f} = ^{2}/_{r}

where o is the distance of the object from the mirror, i is the distance of the image from the mirror, f is the distance from the focal point to the mirror (focal length), and r is the distance between the center of curvature and the mirror (for spherical mirrors)

units = m^{-1}

For spherical mirrors, what does the focal length (f) equal?

f = ^{r}/_{2}

For a plane mirror, the mirror equation becomes:

^{1}/_{o} + ^{1}/_{i }= 0

because at any time the object is at the focal point, the reflected rays will be parallels and the image will be at infinity

Equation to find the magnification of an image for both mirrors and lenses:

m = - ^{i}/_{o}

where o is the distance of the object from the mirror and i is the distance of the image from the mirror or lens

if the absolute value of m is less than 1, the image is reduced

if the absolute value of m is greater than 1, the object is enlarged

For magnification, if the absolute value of m is greater than 1:

the image is enlarged

For magnification, if the absolute value of m is less than 1:

the image is reduced

Refraction is:

the bending of light as it passes from one medium to another and changes speed

In refraction, the speed of light changes depending on:

the density of the medium; this speed change is what causes diffraction

Equation to determine the index of refraction:

n = ^{c}/_{v}

where c is the speed of light in a vacuum (3.8 X 10^{8}), v is the speed of light in the given medium, and n is the index of refraction

In regards to refraction, for all mediums besides air, what are v and n equal to?

v < c because the speed of light is slower in any other medium; n > 1

Equation to find the degree of refraction of a light ray upon entering a new medium:

n_{1}sinθ_{1} = n_{2}sinθ_{2}

theta is always measured with respect to the perpendicular to the boundary

When light enters a medium with a higher index of refraction, it bends toward:

the normal

When lights enters a medium with a lower index of refraction, it bends away from:

the normal

The index of refraction for air:

1

Snell's law states that:

there is an inverse relationship between the index of refraction and the sine of the angle of refraction (measured from the normal)

Total internal reflection occurs when:

light leaving a medium is instead reflected back inside it; it happens when light moves from a medium with a higher index of refraction to a medium with a lower index of refraction with a high angle of incidence

Critical angle:

the minimal angle of incidence at which total internal reflection occurs for that substance; the critical angle is when the refracted angle equals 90 degrees

Equation to determine the critical angle:

derived from Snell's Law

sinθ_{c} = n_{2} / n_{1}

When the incident angle is greater than the critical angle:

total internal reflection occurs and the light incident on the boundary will be reflected back into the original material

What do lenses do?

refract light to form images of objects

Thin, bilaterally symmetric lenses have focal points where?

on each side

Convex lenses are:

converging systems and can produce real, inverted images or virtual, upright images (are like concave mirrors)

Concave lenses are:

diverging systems and will only produce virtual, upright images (are like convex mirrors)

When traveling through a lens, how many times does the light refract?

twice; from air to lens and from lens to air

Equation to determine object distance (o), image distance (i), focal length (f), and magnification (m) for lenses:

^{1}/_{o }+ ^{1}/_{i} = ^{1}/_{f}

m = ^{-i}/_{o}

Equation to determine the focal length in lenses where thickness cannot be ignored:

^{1}/_{f }= (n-1)(^{1}/r_{1} - ^{1}/r_{2})

where n is the index of refraction of the lens material, r_{1 }is the radius of the curvature of the first lens surface, and r_{2} is the radius of curvature of the second lens surface

To simplify sign conventions, think about if the image is on the side it's supposed to be on or not. Mirrors reflect light back; lenses let light pass though. If the image is on the wrong side:

then the image is a virtual image

Equation to determine the power of a lens:

P = ^{1}/_{f}

where f is the focal length in meters; P is positive for converging lenses and negative for diverging lenses

Lenses in contact definition and equation:

a series of lenses with negligible distances between them (contact lenses). They behave as a single lens.

^{1}/_{f} = ^{1}/_{f1} + ^{1}/_{f2} + ^{1}/_{f3} + ...

P = P_{1} + P_{2} + P_{3} + ...

Equation to determine the magnification of a system of lenses not in contact:

M = (m_{1})(m_{2})(m_{3})...

Causes and process of dispersion:

depending on the wavelength of the light, it will bend differently when going through a dispersive medium (i.e. a prism). It is when the speed of light varies with wavelength

Diffraction:

the bending and spreading out of light as it passes through a narrow slit; the light emerges from the narrow slit in a wide arc, not a narrow beam

Equation to determine the location of dark fringes due to single-slit diffraction with a lens:

asinθ = nλ (n = 1, 2, 3,...)

where a is the width of the slit, lambda is the wavelength of the incident wave, and theta is the angle made by the line drawn from the center of the lens to the dark fringe and the line perpendicular to the screen

Interference demonstrates:

the wave/particle duality of light

Young's double-slit experiment shows:

the constructive and deconstructive interference of waves that occur as light passes through a double slit; the interference pattern shows minima and maxima of intensity

Equation to determine the position of maxima on the screen in a double slit experiment:

dsinθ = mλ (m = 0, 1, 2, ...)

where d is the distance between the slits, θ is the angle between the center of the slits and the maxima, λ is the wavelength of the light, and m is the integer representing the order

**USE SMALL ANGLE APPROXIMATION: **

**SINθ ≈ TANθ**

Equation to determine the position of minima on the screen in a double slit experiment:

dsinθ = (m + ^{1}/_{2})λ (m = 0, 1, 2, ...)

where d is the distance between the slits, θ is the angle between the center of the slits and the maxima, λ is the wavelength of the light, and m is the integer representing the order

**USE SMALL ANGLE APPROXIMATION**

**SINθ ****≈ ****TANθ**

Plane polarized light is:

light in which electric fields of al the waves are oriented in the same direction (their electric field vectors are parallel). Light waves exist in 3D, polarizing it limits its oscillations to only 2D