There is something in your eyes...

The object appears the bigger the bigger is the projected image (inverted) on the retina.

The are covered by the image on the retina can be enlarged by increasing the angle. Howeverer, the object can not be placed neither too close (near point, 25 cm in average) nor too far (far point, infinity) way.

Farsighted people have near point further away than 25 cm. This is because the the eye ball is too shor or the cornea is not curved enough. Nearsighted people have far sight closer than infinity. The reason can be too long eye ball or too curved cornea.



Take a look here how to fix farsightedness and nearsightedness.

Converging lens

Object radiates light in all directions. The rays passing through a lens are refracted twice. Converging (convex) lens refracts light such that the rays parallel to principal axis sre refracted to the focal point of the lens.

The focal length is the distance between focal point and the axis of symmetry of the lens. Reciprosal of the focal length is the optical power of the lens in dioptres (D). +4.0 D eye glass is converging lens of 0,25 m focal length.

Try image formation of the converging lens. It is possible to have image/virtual image/no image at all. Examine how is it possible. If the image is formed by real rays of light it is real. The virtual image is created by purely imaginary, mathematical, extensions of the rays of light.

Thin lens equation: 1/f = 1/p + 1/q. Can you derive it using the similar triangles below?

The linear magnification m is determined as: m = hi / ho. Use the similar triangles above to show that m = q / p.

Nature of light and dispersion

White light consist of all different wavelengths in the electromagnetic spectrum. Sun light is white as well as light of the filament lamp.

The light is EM-radiation, where electric anf magnetic fields varies as a function of time. They oscillate in right angles such that the direction of propagation is perpendicular to both fields.

The light travels in vacuum at 300000 km/s, no ether is needed as demonstrated by Michelson and Morley in 1879.

In the medium different colors propagate at different speeds in other words they have different refractive index.

According to Snell law, this leads to different amount of refraction taking place in the boundary between two optically different media.

The white light can be split in colors for example in prism, in diamond or in water droplet.

Transformer and transmission

In an ideal transformer two coils are inductively coupled:

• Same magnetic flux in both primary and secondary coil, the field lines are guided by magnetic material (iron core).
  


• Energy is conserved: power input by primary coil equals to power output of secondary coil.

In reality the iron core is heated due to eddy currents and hysteresis. This can be avoided by laminating the core into individually electrically insulated thin layers.

Look how the transformer acts in step-up or step-down (voltage increased/decresed) mode.

Energy transmission in power lines suffer from losses due to resistance of the cables. Since power dissipated is proportional to current squared it is convenient to use low current but high voltage in the transmission over long distances.

Alternating current (AC)

AC means that the electric current (voltage) is changed both in direction and in magnitude as a function of time. Sinusoidal type is the most common.

In generator (dynamo) the relative orientation of the magnet and the loop is changed leading to change in magnetic flux. Note the two affects of change in rotational speed to the induced current.

Sinusoidal signal is produced by a loop rotating at constant angular is speed in a uniform magnetic field. The magneitude varies between peak values, r.m.s. value being the effective value.

In the AC circuit the power dissipated (to heat etc) in the resistor varies as a function of time, since the current varies. If the mean power over one cycle was equal to the resistor placed in the DC circuit, the DC current would be equal to the r.m.s. value of the AC current.

Hence, if a resistor of 50 ohm is placed in DC circuit it produces heat at the rate of 50 W when 1 A current flowing. In an AC circuit the same 50 W is produced by the same resistor if approximately 1,4 A in peak value is flowing.

Home practical on water flow

PRACTICAL ON THE MOTION OF WATER SURFACE

The aim of the practical is to study the speed of the water surface
in the bottle.


1. Take a plastic bottle which is as cylindrical as possible. Fill the cylindrical part with water and place it standing next to the water sink.

2. Drill a tiny hole (diameter some mm’s) to the wall of the bottle.

3. Let the water flow from the hole and measure the height of the surface as a function of time. Do it as carefully as possible with repetitions. Use cylindrical part of the bottle.

4. Draw height as a function of time.

5. Use the graph to determine the average speed of the water surface over the time period it takes the bottle to empty.

6. Determine the instantaneous speed of the water surface at the time
instant half of the bottle is empty.

7. Make a report on the practical. Remember to
· introduce the instruments
· table the data (units)
· label the axes, title the graph etc.
· show your calculations
· remember hypothesis, conclusion and evaluation of the practical.

Deadline: By the last lesson before exam week.

Lenz law

Lenz law determines the direction of induced electric current in the loop (minus sign in the Faraday law).

An induced current is always in such a direction as to oppose the motion or change causing it.

• If the flux increases, the induced magnetic flux is to decrease the total flux.
  
• If the flux decreases, the induced magnetic flux is to increase the total flux.

The Lenz law is easily understood by means of moving metal rod lying on the U-shaped conductor. Use right hand rule to deduce the direction of e.m.f. The inudced flux is here to out from the page, to oppose the increase of magnetic flux in to the page.

Deduce the direction of induced current in the following cases:

1. Bar magnet, 2. Metal ring, 3. Metal rod

Lenz law is an extension of Newton 3. law applied to electromagnetism. The induced B-field tries to oppose the ultimate reason to the change of the flux. For example:

1. Non-magnetic copper ring induces the magnetic force that bounces back the falling bar magnet and act as counter force to gravity.
2. Magnetic force due to induced eddy currents brakes the fall of a magnet inside the copper tube. Play a video.

Faraday's law

Temporally changing magnetic flux through a conductive loop creates (induces) electromotive force (and current) in the loop. Electromotive force is proportional to negative rate of change of the flux. This is Faraday's law of induction.

In 1831 Michael Faraday was able to show that changing electric current in primary coil creates changing magnetic field that induces current in secondary coil pierced by the same magnetic flux. As a result induced magnetic field was detected by a compass placed in the secondary coil.

The flux changes if B or A or angle or N or all change as a function of time, try with Pick up coil. The brightness of the lamp indicates the strength of the induced current. What about if you vary the rate of change?

Estimate the electric current (GI-current) induced in 400 kV transmission line in the case the vertical component of the geomagnetic field is decreassing from 48400 nT to 47180 nT in a minute. The transmission line makes a polygon in the Southern Finland as shown below. The resistance of the line is 0,9 mohm/km.

Moving charged particle experiences magnetic force

Right-hand rule is one way to remember the direction of magnetic force on charged particle. Current is in the direction of moving positive charge.

Hence, magnetic field exerts magnetic force on the rod carrying electric current.

Definition of 1 A electric current is based on the magnetic force!

The force is perpendicular to both B-field and velocity (cross-product in the formula) and does not increase the speed but change the direction of velocity at any moment. The particle begins to undergo circular path. Try how the different variables affect to the Larmor radius.

Can you conclude anything about the charges and masses of the four particles in the graph below?

Magnetic field

Permanent magnets (bar) or electric magnets (straight wire, solenoid,...) create magnetic field. Moving electric charge (current) gives rise to magnetic field. Unlike electric field lines, the magnetic field lines are closed loops i.e. no magnetic monopole exists. There are always both South pole and North pole.

The magnetic field at any point:

• direction tangential to field line and towards South pole (outside the magnet)


• strength proportional to density of field lines (also called magnetic flux)
  

The geomagnetic field due to plasma streams (volcanic electric currents) inside the Earth and the field geometry pretty similar to the field of gigantic bar magnet. The separation between geomagnetic south and geographic north is about 11 degrees. Solar plasma flow (solar wind) reshapes the dipole field:

In the presence of many fields, the total field is a vector sum of the component fields.

Electric current

The electric current is carried by moving electric charges (free electrons in metals) driven by external electric field (potential difference). The strength of the current depends on

• Number of free electrons in bulk motion
  
• Speed of the bulk motion (typically some cms in an hour)
  
• Collisions between the atoms in thermal motion

Due to the collisions, electrons loose kinetic energy i.e. electrical energy is transformed thermal energy (power dissipation). To maintain the current, work needs to be done at the same rate inside the power supply (cell, battery etc).

The lamp illuminates in five of the following cases. Which?

Electric potential and equipotential surfaces

Positive test charge in the electric field experiences electric force. Moving against the E-field means that work need be done against the force. The work equals to the increase of electric potential energy of the test charge.









As potential energy describes work done to place the charge in the field, the electric potential describes the field itself. For a radial field of spherical charge (no E-field inside the sphere):

• Equipotential surfaces analogous to height contours in the gravity field. Perpendicular to electric field at any point
• No work need to be done in moving a charge along the surface (no displacement in the direction of E-field)
• Potential decreases in the direction of electric field
• Potential is zero infinitely far away from the source of radial field and at any earthed point.

Consider homogenous E-field between two parallel plates separated by distance d. What is the work done in moving charge Q over the potential difference V? If the bottom of the thundercloud and the Earth surface made up the plate pair separated by 1500 m, what would be the potential difference if the electric field was measured to be 25 kN/C.

Electric Field and Coulomb

Stationary electric charge creates static electric field (like mass creates gravitational field).

The geometry of the field depends on the geometry and charge distribution (point, (-s), sphere, line, plate, dipole...)

E-field is described by field lines (here point charges):

• At any point the direction of E-field is a) tangential to field line b) equal to the direction of electric force experienced by a tiny positive test charge.


• Strenth of the field corresponds to the density of field lines.

Coulomb law gives the strength of electric force between two point or spherical charges. Try here if the force obeys Coulomb law.

Electric charge

Any charge (for us..) is a multiple of an elementary charge (-e for electron, +e for proton).

Two ways to create electric charge:

1. Charging by friction. In contact, some atoms (materials) give away an electron more easily than others. Try brushing a sweater by a balloon.
2. Charging by induction. What happens if you move the balloon close to the wall?
   
   

Earthing means connection to infinite source/sink of free electrons.
There is eather attraction or repulsion between two electric cahrges. Can you state the signs of the unknown charges?

Malus and Brewster

In EM-wave, E-field oscillates perpendicular to the propagation.

• Unpolarized wave: E-field oscillates in all possible directions on the plane


• Polarized wave: E-field oscillates along a line (aka linearly or plane polarized)

Polarizer transmits the the component of E-field parallel to its transmission axis. And cuts 50 % of the intensity of unpolarized light.

Malus law: Set the transmission axes of the first and the third polarizers perpendicular to each other. How would you orientate the middle polarizer to have maximum intensity received in the detector? Can you proof it theoretically?

Brewster law: Reflected light is completely polarized if there a right angle between reflected and refracted components. Otherwise it is partially polarized. Rotate the View Angle and take a look to the two components.

Resolution and Rayleigh

Resolution is the minimum separation of two distinguishable objects in an image. Due to wave nature of light, the images get meshed i.e. the diffraction patterns overlap.

Rayleigh criterion: The two images are resolvable if the center peak of one image is exactly over the first minimum of an another image.

Take a look to see how different variables affect to the resolution of optical device.

On a dark night you look down a deserted road and see a distant light growing brighter, brighter... Then it splits into two distinct points of light: the headlights of a car coming towards you! At that moment, how far away is the car?

PRE-IB home practical on thermophysics

Cooling rate

The aim of the practical is to investigate the cooling rate of the tea sample. The temperature (T) of the sample is measured as a function of time (t).

1. The measurement is done at room temperature. Use boiling water to have high initial temperature.
· Take two identical mugs and fill them with 1 dl and 2 dl of tea.
· Read the temperature of the samples every 5 min for over an hour time interval.
· Remember to read the room temperature.

2. Repeat the two measurements outside. Remember to have the same mug and the same initial temperature. Measure the outside temperature.

3. Plot all the data in one (t,T) -system of coordinates.
· Indicate the different data sets
· Draw lines of best fit by eye to the data sets
· Determine the average cooling rate (unit: °Cs-1) for each sample
· Determine the cooling rate at the time t = 0,5 h for both 2 dl samples.

4. Answer briefly:
· How does the cooling rate change as a function of time?
· How does the mass affect on the cooling rate?
· How does the outside temperature affect on the cooling rate?
· Can you explain the shape of the curve?
· Are there any other variables affecting to the cooling rate? How would you investigate their contribution?

Single slit diffraction

Diffraction takes place at any slit, obstacle, edge... Relative size of aperture to the wavelength defines the amount of diffraction in a slit.

The diffraction pattern consist of bright and dark fringes:

• Bright due to constructive interference: path difference between the waves is a multiple of wavelength (central fringe, exactly zero)


• Dark due to destructive interference: path difference between the waves is a multiple of half wavelength (first dark fringes around central fringe, exactly one half of a wavelength).

Check the relationship between the location of dark fringes, wavelength and aperture.

Standing Waves

As two waves moving in opposite directions interference the standing wave is formed. For example interference of wave with its reflection

• Does not propagate but remains stationary i.e. no net propagation of energy
• The amplitude is a superposition of its componenets
• Node: no motion. Antinode: maximum motion

Longitudal standing waves are present in flute, pipe, clarinet etc.. in which the air column in the tube resonates at some characteristic frequencies (harmonics) of the external sound. The longest possible wavelength is called first harmonic (fundamental)

Doppler Effect

You know the sound of a car passing by changes. Not only the intensity (loudness), but also the frequency (wavelength).

• As the source comes towards the observer larger frequency (shorter wavelength) is heard by the observer


• As the source moves away from the observer smaller frequency (longer wavelength) is heard by the observer

Try the applet and take a look to separation of the wavefronts (wavelength).
What happens if the source is moving at the spped of sound or even at a supersonic speed?

The effect takes place if the observer moves also. Or both move. As long as they are in relative motion.

Diffraction

Waves go behind the corners, the legendary ripple tank finally works. No way in real world...

Diffraction patterns are due to interference of different waves, in other words the superposition of the waves.

Try that. Pick up 4 points of minimum intensity and another 4 of maximum intensity. What are the path differences of the two waves in different cases?

• The constructive interference (max intensity) takes place when the path difference is a multiple of the wavelengths.
• How about destructive interference?

There are two loudspeakers in the opposite ends of the room sending 440 Hz. Consider you walk on the line joining the loudspeakers. Describe the sound you hear. What is the minimum distance between the points you do not hear anything at all?

Refraction

Pretty many of you have faced with folded or even uncontinous drinking straw in the soda glass.



































Think about soldiers marching in rows from firm ground to muddy ground. They keep on walking in the same rhythm (frequency).

• How do change the length of the step and the speed? Analogue to wave motion!


• Snell law gives the change in the direction.

Try the explanation by Huygen's principle.

Wave characteristics part 2

As the two pulses meet the result (sum pulse) can be understood by superposition principle. The interference is

• constructive, if the pulses are in phase
• destructive, if the pulses are in opposite phase.

At the boundary between the two media, the pulse is both reflected and refracted (some of the pulse energy is absorped in the end).

1. Reflection

• Phase change (to opposite) takes place, if the pulse is reflected from fixed end
• No phase change, if the pulse is reflected from free end.

2. Refraction

• Take a look to speed, wavelength, phase and amplitude...

Wave characteristics part 1

It's not the meat, it is the motion..

• The wave carrier (air, string, EM-fields etc) do not propagate, but the motion and energy do. Wind does not push all the water to one end of the lake.
• Transverse waves: oscillations perpendicular to the direction of propagation (light, surface waves etc). Longitudinal waves: oscillations parallel to propagation (sound).
• 5 oceanic waves, roughly 5o m from crest to crest, hit the sea shore in a minute. How fast they are moving?