Photography with use of polaroid

pic taken from :http://www.cs.mtu.edu
The polarizer aligned in a direction perpendicular to the direction of reflected light is able to cut the intensity of light reflected giving rise to a good view of fish in the water.

Single slit to ensure coherence

pic taken from quantumweirdness.wordpress.com
The single slit placed before the double slit diffract the single beam of light to ensure coherence at the double slit. Without the slit the light reaching the doule slit is not coherent.

Polarizer

A polarizing filter blocks all light of one polarization, passes all light of the perpendicular polarization, and passes some but not all of the light for in-between polarizations, as is depicted in the sketch below. This lets the polarizing filter affect the appearance of a scene that has polarized light in it.pic taken from www.edbergphoto.com

Interference of sound

A)What is the lowest frequency for which constructive interference occurs at point Q?
Wavelength of sound = 1 m

B)What is the lowest frequency for which destructive interference occurs at point Q?
Wavelength of sound = 2 m

Diffraction around island

This is the spreading out of waves when they pass an obstacle or through a gap. Diffraction occurs the most when the gap is of similar size to the wavelength of the wave. Diffraction can occur with any wave: water waves, light, sound, radio waves etc.
The diffraction of X-rays can be used to study the structure of crystals. This is because the wavelength of the X-rays is similar in size to the 'gaps' between the crystal’s molecules.
When parallel waves approach a gap in an obstacle, they are diffracted through the gap. A great example of this is shown in this picture. The waves are coming from the bottom right of the image and notice how they are diffracted through the gap between the islands. extracted from : http://www.suntrek.org/factary/d.shtml

Diffraction of radio waves

The bending, called diffraction, results in a change of direction of part of the wave energy from the normal line-of-sight path. This change makes it possible to receive energy around the edges of an obstacle as shown in view A or at some distances below the highest point of an obstruction, as shown in view B. The principal effect of diffraction extends the radio range beyond the visible horizon. In certain cases, by using high power and very low frequencies, radio waves can be made to encircle the Earth by diffraction...extracted from : www.tpub.com

Overlapping spectrum

Overlapping normally does not occur at first order. See the overlapping of 2nd and 3rd order , can you detect where it has overlapped !

Overlapping orders Photography

Click on link to see what overlapping looks like . Red and blue lines should not be close together as they are at opposite end of the spectrum . This picture shows the blue line next to red line . The third order blue overlap the second order red line . The overlap here is overtaking. Sometimes overlapping can mean exist at the same location(angle) and the composite colour will occur.

Young's double slit

The Young's double slit formula is only an approximation ! The approximation is that angle is small then tan (angle) =x/D and sin (angle)= lamda/a are approximately equal. Hence the equation lamda= ax/D.
If you use dsin(angle)=lamda (for n =1) and if angle is small it would be approximately tan(angle) = x/D and hence dx/D =lamda which is ax/D as a is spacing between slits.
It is therefore important to use Young's double slit with caution. In general it is applicable to most questions found with 2 source and a screen a large distance from it.
Link provide a derivation of young's double slit formula.

How intensity affects interference

In a normal situation the light arriving from double slits are assumed to be of the same intensity. Constructive interference : A + A = 2A,Destructive interference :A - A = 0. The effect of CI and DI is bright and dark fringes .
In a Young's double slit expt, one light source passing a single slit and then a double slit will therefore ensure that the intensity are the same from both slits to produce observable interference.
Further from the central bright fringes , the intensity of light arriving from the two slits will not be the same as one will be closer than the other. CI and DI will not be as stated above as there will not be complete cancellation of the amplitudes from the 2 slits. The fringes will be less contrasting as the dark fringe will not be completely dark.

Intensity - two different application

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(Intensity is proportional to square of amplitude )vs (Intensity is inversely proportional to square of radius)
The two are not related except that they are referring to intensity.
First case : Intensity at a location is proportional to amplitude of wave at the same location. No possibility of confusion.
Second case: Do not use the relationship if possible. Use only Intensity is equal to Power divide area. If the power of source is the same then only I is proportional to radius square (area of the sphere)
Caution: Intensity of the point source has no meaning. It should be intensity at a certain distance from the point source
If intensity at certain distance from the point source is known. Then the power on a surface area S is equal to IS.Take note that all of the area S must be of the same distance from the point source. This will mean that S must be a curved surface!If S is not curved than it got to be very very small such that its intensity over the whole surface is constant.
Point to ponder: Imagine the projector as a point source and the screen is flat on the wall. Do you have the same intensity throughout the screen. A good projector may make it hard to detect. Maybe OHP may be a better illustration.

Stationary wave in sound

High pressure occur at node and low pressure at antinode.
Imagine standing in a queque. You are the node i.e you dont move . To the left and right of a node is displacement in opposite sign (direction) So in the queque the person if front of you will push towards you and so did the person behind you also did the same . Dont you feel squashed up! Particles in that squashed up location is the node having high pressure.

Stationary wave formation

Two wave of same amplitude , velocity and frequency travelling in opposite direction superpose to form stationary wave. Know the resulting wave well enough. How the two waves are like at any moment is not necessary . The resulting waveform must be known completely. Some points about the resultant waveform.
1. Amplitude differ : largest at antinode and zero at node
2. Same phase: Every particle between 2 nodes have the same phase .
3. Antiphase: Particles that are in phase are antiphase with particles in the adjacent nodes (segments)
4. Same period: Except for the nodes, every particle have the same period.
5. Velocity differ: Particles have the largest velocity at the antinode (at equilibrium - SHM )
6.In longitudinal wave the high pressure occurs at the node and low pressure at the anitnode. *See next entry

Intensity proportional to square of amplitude

image by comsol model gallery
Intensity mentioned in superposition does not require the formula power over area but the intensity is inversely proportional to r square. A simpler understanding like Intensity is lower because the distance is further is often sufficient for this part of the topic.
In fact to simplify the above fact, questions require you to take the Intensity as I (the same value) eventhough one source is nearer than the other source. If this is not the case , the calculation I would require power divide by area of sphere of radius r.
Straight forward example:
Constructive interference at P : Each source providing intensity I at P(eventhough P may not be same distance from the two sources) .Take amplitude of I to be A, constructive interference will result in waveform having 2A. Now using ratio, the resultant intensity will be 4I
Destructive interference at Q: Take amplitude to be A from each source, but cancel out due to destructive interference , resultant intensity 0.
Not so straight forward case:
If two coherent waves of intensities I and 2I meet in phase at a point, what is the resultant intensity at that point. This require perserverance mathematically!
If I has amplitude A, the 2I has an amplitude of 1.414A. Use ratio to deduce.
Now the resultant amplitude A' =2.414 A , for constructive interference.
Use ratio again , I has amplitude A , now A' has intensity I'.
The answer I' =5.83I
Another not so straight forward case:
If the wave from one source S1 is I having amplitude A and the other source S2 has amplitude 1.5A.
What is the resulant intensity at P and Q, where there is constructive interference and destructive interference respectively?
At P: Amplitude is 2.5A, intensity I'= 6.25I
At Q : Amplitude is 0.5A, intensity I"= o.25 I.

To sum up, intensity is dependent on r and amplitude.These two relationships are to be treated independently.

Phase difference between fringes

Young's double slit produces fringe patterns that are equally spaced having fringe separation, x. The phase difference of the light arriving at n=0 or n=1 or n=2 or n=3 etc are said to have zero phase difference or phase angle = 0. The path difference of the light arriving at n = 0 is zero, for n=1 is one wavelength , and n=2 is two wavelength, n=3 is three wavelength etc.

Apart from these very distinct cases , what is the phase difference for a location mid pt between n=2 and n=3 bright fringes. If n=2 and n=3 has a phase angle =0 or 360', then mid point will have to be 180'. I state degree because I cant find pi on my keyboard. The path difference will have to be 2.5 wavelength.

For another less obvious case where it is neither bright nor dark, and located halfway between a bright and dark fringe, then the phase angle would be halved again to 90' and the path difference will have to be 2.25 wavelength or 2.75 wavelength since we are looking between n=2 and n=3.

KE and PE in stationary waves

The diagram shows a stationary wave at the time(t=0) when all the particles are at rest! Therefore its kinetic energy is zero and its potential energy is maximum. The same its true when the wave assume the other extreme position as shown by the faint line at t= T/2. In the middle between these two extreme line at t=T/4 . the particles have maximum ke except the nodes. Therefore the energy of the stationary wave has potential energy = 0 and kinetic energy is maximum. The stationary wave in the other times are partly ke and pe but the total energy remains constant. The energy stays within the stationary wave and just exchanges between ke and pe in time. It 's as though the energy is trapped within the stationary wave and not propagated like progressive wave. It's easier to remember that the p.e is max. by looking at the wave as if it is a string that is stretched to a maximum at the two extremes. When the string is straight (least stretched) the p.e=0 and k.e max.

Stationary sound wave

Nodes and antinodes in stationary wave are detected as pressure change above and below the normal pressure. Consider air molecules to have normal pressure without the sound waves passing throught it. When stationary waves are formed in sound wave , there exist nodes and antinodes. Take a look at the nodes, a particle with no displacement. The particle on its left and right are moving in the opposite direction (180 degrees out of phase). The particle at the node is squashed by its two neighbouring particle. Just imagine standing in a queue and being pushed by someone in front and someone behind you . This point becomes a higher than normal pressure point. At the antinode , even though the displacement is large , it's neighbouring particles are moving in the same direction as the antinode particle but with a smaller displacement. Therefor the pressure change is minimum.

Ingredients in light

When you use artificial lighting, you may be unhappy with the effects of different types of bulb. The variety of light of unique wavelengths are not the same as sunlight which gives us a continous range of colours. In order to investigate the wavelengths of light , a narrow beam is made to pass through diffraction grating that has the ability to split them and direct the different wavelengths to different angles so that they become visible. Imagine if you were to eat something really tasty, how could you find out what goes in it. With diffraction grating, we can solve the mystery as to what the light is made up of. To our suprise a seemingly "blue" light has a tinge of red or green or violet or many shades of blue.Using the formula dsin(teta)= n(lamda) . Consider n=1 , different wavelengths can be viewed at different angles. You can look through a light spectrometer in your lab to investigate the ingredients of light from different types of bulb.

Damping graphs

Damping graphs has nothing to do with resonance. Resonance is affected by damping for sure. Draw light damping , heavy damping and critical damping in the same axes so that you know effect of damping on the same system. The graph above shows the desirable effect of shock absorbers to achieve critical damping . If it oscillate you can say it's underdamped.If the spring is too stiff (k value too large) than it's overdamped. Just enough damping, returning to equilibrium in the shortest time possible T/4, it's critical damping. Shock absorbers is an important component in cars , bicycles and in fact all vehicles including the aeroplane. Shock absorbers are found in washing machine, blender , etc. Watch this video showing critical damping , as the barrel returns to its original position in the quickest possible time after firing.Video below is taken from this link : reliability.equipment.com

Stationary waves from guitar strings

The lowest frequency that can be produced is called the fundamental frequency and it has the greatest amplitude. I will therefore decide which note (f) you are listening to. The next higher frequency is twice (2X) the fundamental but has a smaller amplitude. The next higher frequency has thrice (3X) the fundamental but has a smaller amplitude, the list go on depending of the type of musical instrument. Sum up all these frequencies you get a unique sound of guitar that doesn't sound like a tuning fork. The fundamental frequency is only changed in its shape of waveform but not the frequency.