Section 4: Waves and Optics Flashcards
Geometric optics
A description of light as ‘rays’ that propagate in straight lines
Only an approximation
Assumes there’s an infinite no of rays originating form each point on an object
Laws of reflection
Angle of incidence = angle of reflection
The incident ray, the reflected ray and normal all lie in the same plane. This plane is perpendicular to the surface
What is a ‘normal’
An imaginary line perpedicular to a surface
Nature of images in a plane mirror
Upright
Same size
Virtual
Equally far behind the mirror as the object is in front
Define virtual image
Constructed out of virtual rays traced back behind the mirror to a point of origin
Concave mirror
Converging mirror
Caves inwards
Focal point in front of mirror
Convex mirror
Diverging mirror
Bulges outwards
Virtual focal point behind mirror
What is ‘n’
Index of refraction
Snell’s law of refraction
When n2 > n1, light bends toward the normal
When n1 > n2, light behinds away from the normal
Total internal reflection - θc
Critical angle, where angle of refraction is 90°
When exceeded, there is no refracted light - all the incident light is reflected back into the medium which it came from
Convex mirror - nature of image
Virtual
Erect/upright
Diminished
Concave mirror - nature of image
If further out than f:
Real
Inverted
Size depends where image is
If at f, real nor virtual rays converge –> no image (infinity)
If closer than f:
Virtual
Erect
Enlarged
Convex lens - nature of image
Depends where the object is
Concave lens - nature of image
Virtual
Upright
Reduced
Same side as object
Multiple lenses
Overall magnification is the product of the magnification of the 2 lenses
Convex lens - how do rays refract
Towards focal point on opposite side of object
Concave lens - how do rays refract
Away from focal point on opposite side of object (and so virtual rays towards the focal point on same side of object)
Real image
An image that can be projected onto a screen
Virtual images
Where rays appear to originate from a common point
Image can’t be projected onto a screen since rays don’t focus
Thin lenses
Form images through refraction of light
Converging lens/mirror
Convex lens
Concave mirror
Diverging lens/mirror
Concave lens
Convex mirror
d(0)
Object distance
Always +ve for real objects
d(i)
Image distance
Positive for real images
Negative for virtual images
Focal length (f)
Focal length for converging mirror/lens is +ve
Focal length for diverging mirror/lens is -ve
M
Magnification
+ve for upright image
-ve for inverted image
Double lens - 1st image ends up on other side of second lens
Use a -ve sign for d(o.2) in the equation
Wave
A disturbance that moves itself and energy but not matter from one place to another in a medium
Particles in the medium vibrate about their original position
Transverse waves
Particlesi n the medium move in a direction perpendicular to the direction of travel of the wave
Longitudinal waves
Particles in the medium move in a direction parallel to the direction of travel of the wave
Most waves in nature are _____
Periodic
i.e. they repeat themselves
Wavelength (λ)
Distance from a point on the wave to the next corresponding point on the wave
Units: m
Amplitude (A)
Max displacement from the centre line (equilibrium position)
Units: appropriate to type of wave, e.g. m, V, Pa
Period (T)
Time for one complete vibration
Units: s
Frequency (f)
No of vibrations per second
Units: Hz
Speed (v)
Rate of movement (propagation) of a wave
Phase
Describes at what stage of the cycle as wave is; going up or down, from the reference value
In phase
Particles in a wave considered to be in phase when they execute the same motion (same stage of their cycle) at the same time
180 degrees out of phase
Half a cycle out of phase
Execute the exact opp motion at the same time
Intensity
Power per unit area
Decibel (dB) scale
Used to compare intensities
Intensity and dB
Adding 10 dB = multiplying I by 10
3dB is approx 2x intensity
Doppler effect
The change in the observed f of a wave due to the motion of the wave source relative to the observer
Doppler effect - source moving towards observer
Increase in f, decrease in wavelength
Doppler effect - source moving away from observer
Decrease in f, increase in wavelength
Principle of superposition
The resultant waveform when diff waves meet at the same point in space at the same time is the sum of their individual displacements (heights)
Constructive interference
2 waves of identical f and A arriving at the same point exactly in phase
Resultant wave has twice the A but same f and wavelength
Destructive interference
2 waves of identical f and A arriving at the same point exactly out of phase
Resultant wave has zero amplitude
Partial destructive interference
2 waves of identical f but diff A arriving at the same point exactly out of phase
Resultant wave has same wavelength and f, but its A is the difference of the amplitudes of the individual waves
Beats
Where 2 waves have slightly diff frequencies and superimpose
Overall amplitude = beat frequency f(B)
Natural frequency
The f at which an object vibrates when it’s set to vibrate and then left free
Forced vibration
An object is forced to vibrate at a certain f by constantly applying a periodic force
Forced vibration - amplitude
Depends on frequency of the forcing
If forced at natural f, the A can grow huge
Resonance
Tendency of a system to oscillate at larger amplitudes at some f than others
Max amplitude = when system forced to vibrate at its natural frequency = at resonance
Avoiding resonance
Tuned mass dampers stabilise against violent motion caused by forced vibrations
Diffraction
The bending of a wave around an obstacle or the edges of an opening
Coherent sources
Sources that maintain the constant phase difference
2 wave sources vibrating in phase
PD = 0 or integer --> constrictive interference PD = 1/2 wavelength --> destructive interference
2 wave sources vibrating out of phase
PD = 1/2 wavelength --> constructive interference PD = 0 or integer --> destructive interference
Light - maxima and minima
Maxima = bright fringes, PD = 0 or integer Minima = dark fringes, PD = half integer
Rayleigh Criterion
2-point objects are just resolved when the first dark fringe in the diffraction pattern of one falls directly on the central bright fringe in the diffraction pattern of the other
Brester’s law - incident angles other than 0
For incident angles other than 0, unpolarised light becomes partially polarised in reflecting from a non-metallic surface
Brewster’s law - Brewster angle
When unpolarised light is incident on a non-metallic surface at the Brewster angle (θB), the reflected light is 100% polarised in the direction parallel to the surface
The angle between the reflected and refracted rays is 90 degrees
(AZ) X
A = nucleon number; no of protons and neutrons Z = proton number; no of protons
Radioactive decay - assumption
The probability that any one nucleus out of N nuclei decays in any one second is a constant λ (decay constant)
Half-life of a radioactive nuclide
The time taken for the no of undecayed nuclei to be reduce to half its original number
Nucleus: A = ?
A = Z + N (no of protons + no of neutrons)
Isotopes
Nuclei that contain the same no of protons but diff no of neutrons
Strong nuclear force
The mutual repulsion of protons tends to push the nucleus apart
The strong nuclear F acts over short ranges and binds the protons and neutrons tgt
Nuclear stability
As the nuclei gets larger, more neutrons are required for stability
Radioactivity
Where unstable nuclei can break apart on their own with a predictable probability
Alpha decay (α)
The nucleus ejects a He nucleus to become a smaller and more stable nucleus
Beta decay (β)
A neutron is converted to a proton (or vice versa) to become a more stable nucleus
Releases energy - carried away by a neutrino
Gamma decay (γ)
The nucleus gives off energy in the form of a gamma ray to reach a lower energy state
