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.