Phys6 - Light & Optics

• constructive: waves are in phase (additive)
• destructive: waves are out of phase (if equal in amplitude waves cancel out perfectly)

• two light waves hit the same spot:
• if in phase → constructive overlap
• if out of phase → destructive overlap

• If light wavelengths are different from each other by some variation of half a wavelength (eg. 1/2, 3/2, etc.) then the resulting light spot will appear DARK →
• *a dark light spot signifies DEstructive interference
• m = any integer starting with 0 (1, 2, 3, etc.)

• if the “distance” a light wavelength travels is different from another by some variation of an integer of a wavelength (eg. 1, 2, 3, etc.) then the resulting light spot where the 2 wavelengths converge will appear BRIGHT →
• *a bright light spot signifies CONstructive interference

• a surface with slits equidistant all the way across it
• if light is shone through the surface there are many slits which it can pass through
• d = distance between adjacent slits
• equation for diffraction grating is the same as for just a double slit system: dsinθ = m*λ

• c_vac = 3 * 10⁸ m/s
• similar value for the speed of light in air

• n = c_vac / v_med
• c_vac: speed of light in a vacuum
• v_med: velocity of light in whatever medium
• v_med will NEVER be larger than c_vac b/c light will never travel faster than it does in a vacuum
• therefore the ratio for n will always be bigger than 1
• n ~ 1 for air
• n ~ 1.33 for water

it becomes INVERTED

• smear of all wavelengths of light in the visible spectrum
• if you REMOVE a color from white light (eg. due to destructive interference?) what results is that color’s complimentary color across from it on the color wheel

• if a mirror is concave → it’s converging
• if a mirror is convex → it’s diverging

• if a lens is convex → it’s converging
• if a mirror is concave → it’s diverging

• always equal to exactly 1/2 the radius of curvature
• f = 1/2r

• 1/f = diopters
• focal distance HAS to be in meters
• 1 over the focal distance = Diopters (D) → which corresponds to the strength of a lens

• 1. focal length (f) [f = 1/2r]
• 2. strength of the lens in Diopters [D = 1/f]

• if the image comes out below the principle axis → it’s inverted (upside down)
• if the image comes out above the principle axis → it’s upright

• if light rays truly converge at di or a certain point → the image is Real
• if light rays do not truly converge at any certain point → the image is Virtual

• can remember using the mnemonics:
• IR spec: Inverted, Real
• UV light: Upright, Virtual
• (also remember just it’s counterintuitive - weird opposites)

• 1/f = 1/d_o + 1/d_i
• d_i: distance from mirror to the image
• d_o: distance from mirror to the object

• m = h_i / h_o or m = – d_i / d_o
• h_i: height of the image
• h_o: height of the object

• object will ALWAYS be out in front of the mirror → d_o is positive (+d_o)
• if the image is REAL (i.e. the light rays that form the image actually converge) → d_i is positive (+d_i)
• however if the image is virtual (i.e. the light rays that form the image NEVER actually converge) → d_i is negative (–d_i)

• if m is positive → then the image in question is upright
• if m is negative → then the image is upside-down inverted
• if the absolute value of m is bigger than 1 → then the image appears bigger than the original object
• if the absolute value of m is smaller than 1 (eg. 0.5) → then the image appears smaller than the object

the focal distance for a diverging MIRROR is NEGATIVE (-f)

1. Upright

2. Virtual (UV)

3. smaller than the original object [regardless of whether the do is smaller or larger than the focal distance (inside or outside f)]

• always makes the resulting image look smaller

• always results in a Upright, Virtual image

• when you’re looking at an image in a mirror or through a lens & it appears a little bit FUZZY
• there are 2 explanations for why aberrations occur → both have to do with light rays not converging on a single point to form a clear focused image*

light rays that pass through the outer edges of a lens (aka farther away from the principle axis) don’t quite converge exactly where the image forms? → results in a blurry image

• as light of different colors passes through the medium of a lens, the light rays get refracted by the lens
• the indices of refraction for different colors varies depending of the color → this causes some colors to be refracted more or less (angle of refraction differs)
• usually what results is the edge of the image appear fuzzily colored