WAVES

Energy is often transferred from place to place by waves. These are called progressive or traveling waves. Waves can be of two types :

Transverse: transverse waves are ones in which the displacement of the particles is at right angles to the direction of travel of the wave motion.

This means that the waves move up and down whilst they move forward ( up and

down is at right angles to forward). The particles are the ones which make up the

wave. Displacement refers to the up and down movement. An example of a

transversal wave is a water wave.

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Longitudinal: longitudinal waves are ones in which the displacement of the particles is in line with or parallel to the direction of travel of the wave motion.

This means that the waves move slightly forwards and backwards whilst they

move forward. (in line with and parallel to means backwards and forwards) An

example of a longitudinal wave is a sound wave.

The object producing the wave doesn’t actually move.

Consider a rope held by two people at either end. If one of them moves the rope

up and down, you will see transversal waves going up and down. The rope is still

held by the two people and it doesn’t move forward.

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The Ripple Tank

A ripple tank is a tray filled with water. Waves can be produced by disturbing the

water and then studied. When waves are produced, you can see that they are

transversal because they move up and down.

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The high parts are called crests or peaks and the low parts are called troughs.

The distance any particle is from the average water level (the water level when

the water is still with no waves) is called the displacement.

The highest displacement is the highest point which is at the top of the crest, and

the lowest point which is at the bottom of the through. (these two displacements

are equal). This maximum displacement is called the amplitude a of the wave.

Imagine a wave starting from a crest going down to a trough and back up to a

crest. Then it has to start all over again. This distance from crest to crest ( or

from trough to trough) is called the wavelength of the wave.

The wavelength is the distance between two identical points on consecutive

waves

The units of wavelength are m ( or cm )

One can count how many cycles ( up and down) a wave performs in one second.

This is called the frequency f of the wave.

The units of frequency are called hertz (Hz).

Frequency is the number of complete oscillations in 1 second

When the speed of a wave remains the same, the frequency increases when the

wavelength decreases and vice versa. One can find the speed, frequency or

wavelength of a wave if one knows the other two using the equation

Wave speed (v) = frequency (f) x wavelength (),m/s = Hz x m

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eg : if the speed of a wave is 200m/s and the wavelength is 1.6m, what is the

frequency of the wave ?

v = f x 200 = f x 1.6 200 = 1.6f

200= f 1.6

125 Hz = f

Reflection and Refraction

Reflection

Waves can be produced in a ripple tank. If a straight object is placed at the other

end, the waves will hit this object and go back. This is called reflection.

The object causing the reflection is called a mirror even though it is not

necessarily a mirror we can see ourselves in.

Usually, waves are drawn as straight lines perpendicular to the direction of

motion. These are called wavefronts. However they can also be circular

If the mirror is parallel to the wavefronts, then the waves are reflected in the

same direction they came from.

If the mirror is at an angle to the wavefronts, the waves will also be reflected at

an angle.

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In reflection, there is no change in velocity, frequency or wavelength. There is only a change in direction if the mirror/barrier is at an angle.

Refraction

If a glass sheet is placed in the tank, that part of the tank has been made

shallower. This will have an effect on the waves called refraction.

It can be seen that waves travel more slowly in the shallow water. Therefore the

speed is less. It can also be seen that the wavelength also decreases. However

the frequency does not. The equation v = f still holds.

If the sheet of glass is placed in line with the wavefronts, the waves will continue

moving in the same direction ( slower and with a smaller wavelength).

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However, if the glass sheet is placed at an angle to the wavefronts, the refracted

waves will also move at an angle to the original waves.

In refraction there is no change in the frequency. However the velocity and the wavelength will decrease. If the obstacle is at an angle, there will also be a change in direction.

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Diffraction

If a straight obstacle with a small gap is placed in the ripple tank, the waves will

pass through the gap without a change of speed, frequency or wavelength.

However, they might spread out. This effect is called diffraction.

If the gap is considerably wider than the wavelength of the wave, the waves

coming out of the gap will not be diffracted ( will not spread out) except for slight

curving at the ends. This is called rectilinear propagation.

If the width of the gap is about the same size (or smaller) as the wavelength, the

waves will be diffracted and the wavefronts will become circular.

In diffraction, there is no change in velocity, frequency or wavelength.

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LIGHT

Visible light is a form of energy in the form of waves that is detected by the eye. Objects which produce visible light are called luminous sources (sun, stars, lamps etc…) This visible light enables us to see objects by falling on the objects and then being reflected into our eyes. These objects are said to be illuminated.

Most surfaces are uneven, or contain particles that scatter light. As a result, they reflect light in all directions. This reflection is called diffuse reflection. However, mirrors are smooth and shiny. When they reflect light, the reflection is regular reflection.

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Objects which produce regular reflection are usually shiny or glossy. This makes it difficult to read any writing on them. ( your whiteboard!!!)

Objects which produce diffuse reflection are usually matt. This makes it easier to read any writing on them ( normal paper)

Features of light

1. Light is a form of radiation. It is a transverse wave of wavelength of about

1 mm. It is part of a larger electromagnetic spectrum. 20002. Light travels in straight lines. It is called rectilinear.3. Light transfers energy. Energy is needed to produce light.

Materials gain energy when they absorb light.4. Light can travel through empty space (vacuum) Being part of the

electromagnetic spectrum, light does not need a medium to travel. This is why light can reach us from the sun and other stars.

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5. Light waves all travel at the same very high speed of 3 x 108m/s. nothing can travel faster than this ( till now!).

Rays are narrow beams of light which are easily seen and hence are used in experiments. A raybox is a box with a narrow slit. A lamp is placed inside the box and a ray of light emerges from the slit. This ray is straight and if an obstacle is placed in its path, it will not curve

Reflection

Light can be reflected by plane (flat) mirrors.Place a plane mirror standing upright and shine a ray at an angle to the mirror. This ray is called the incident ray. The ray will be reflected back at the same angle. This is called the reflected ray.

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Li is the angle of incidenceLr is the angle of reflection.

Angle of incidence = angle of reflection (same as water waves)In this way, the ray is turned (deviated) by twice the angle of incidence.

IMPORTANT : Rays of light must always be marked with an arrow to show their direction

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There are two laws of reflection. 1. the angle of incidence is equal to the angle of reflection2. the incident ray, the reflected ray and the normal all line in the

plane of the paper.

Image

When an object is placed in front of a mirror, what is seen in the mirror is called the image. The image in a plane mirror is:

1. Virtual ( imaginary ---not real)2. Laterally inverted (same side up but left and right sides

reversed)3. Upright4. Same size as object5. As far behind the mirror as the object is in front.

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PeriscopePeriscopes use two mirrors to enable one to see above an obstacle. The mirrors are placed such that the rays are incident at 45 at each mirror so that at each mirror the rays are turned by 90. Since the image has been turned twice, the final image is not inverted.

When a high degree of accuracy is needed, prisms are used instead of mirrors.

This will be discussed later.

Refraction

When you put a spoon inside a glass of water, the spoon appears to be bent.

This effect is called refraction. This is what happens when rays traveling in one

medium ( eg. Air) enter another medium ( eg. Glass)

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This incident ray meets the glass block at an angle i to the normal.

The normal is a line at right angles to the block at the point where the ray meets

the block.

ALL ANGLES ARE MEASURED WITH RESPECT TO THE NORMAL

When the ray enters the glass block, it is slowed down. This will make the ray

bend towards the normal. It will travel inside the glass block in this path at a

slower speed. When the ray emerges from the block at the other end, it speeds up again and hence bends away from the normal in the original direction.

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Li is called the angle of incidence

Lr is called the angle of refraction

Rays of light traveling from air into glass are bent or refracted towards the normal.Rays of light traveling from glass into air are refracted away from the normal.

Refractive index

We saw that when a ray enters glass ( a denser medium), the ray bends towards

the normal and slows down. The ratio of the speed of light in air and the speed of

light in the second medium is called the refractive index of that medium

Refractive index = speed of light in air

of a substance speed of light in the substance

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Note: Since nothing can travel faster than light, the numerator is always larger

than the denominator and so the refractive index is always larger than 1.

The larger the refractive index, the more the light ray changes direction.

Total internal reflection

We saw that when a ray emerges from glass into air, the ray is refracted away

from the normal. The angle of incidence can be increased so that every time the

refracted angle increases as well.

However you will reach a point where the refracted angle will be 90 which is the

angle between the normal and the block, so the ray will travel on the edge of the

glass block. This is called the critical case. The angle of incidence at this point is

called the critical angle C. if the angle of incidence is increased more ( larger

than C), the ray will be trapped inside the glass block are will not be refracted at

all. It will instead be reflected inside the glass block itself.

This is called total internal reflection.

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Total internal reflection takes place only when

1. the rays are traveling in a dense medium towards a less dense medium

2. the angle of incidence is greater than the critical angle.

NOTE: The critical angle of glass is about 42º

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From the critical angle, the refractive index of the medium can be found

Refractive index = 1 . Sine C

IMP :When a ray enters a semicircular glass block aimed at the centre, the angle

of incidence is 0˚ ( angle with glass is 90˚). This means that there will be no

refraction at this point. Refraction will take place when the ray hits the straight

side of the semicircular glass block.

Totally reflecting prisms

A triangular glass prism is a glass block whose face is in the shape of a triangle.

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Consider a prism whose angles are 45 ,45 and 90.

When a ray is incident at right angles to one of the sides (not the hypotenuse),

the angle of incidence is 0, hence the ray passes straight through without it

being refracted. Then it hits the hypotenuse side at 45. Since this is larger than

the critical angle of glass ( C=42), total internal reflection will take place (no ray

will leave the glass). This reflected ray will then hit the bottom side at right angles

( angle of incidence =0), and will leave the glass without it being refracted. In this

case the original ray has been turned by 90.

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This effect is usually used in periscopes instead of plane mirrors because prisms

are more efficient than mirrors. The reasons are:

1. Mirrors reflect less light than a totally reflecting prism

2. The silvering on mirrors can get damaged easily

3. Since mirrors have a layer of glass over the silvering, multiple reflections

due to the glass and the silvering can occur.

The prism known as the 45-45-90 prism used above can be used in other

ways.

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This time, the two short sides are used

to turn the ray by 90 each which means

that the ray will be turned by a total of 180.

Uses:

1. Diamonds are cut in a similar way so that the rays entering the diamonds

are totally internally reflected to make the diamond shine more.

2. Rear reflectors (on cars and bicycles). The light coming from a headlamp

of a moving car will be reflected back so the driver will know that there is

something in front of him.

3. Cats’ eyes. Same as number 2

4. Binoculars. Reflecting prisms are used to shorten the instrument and

produce an upright image.

Optical fibre

An optical fibre is made of a long flexible glass tube. When rays enter the tube

through one side, the incident ray will be greater than the critical angle, so total

internal reflection will occur. The ray will thus keep on being reflected inside the

tube without it escaping until it reaches the end of the tube. These fibres are

usually grouped in bundles,

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Optical fibres can carry telephone calls. The signals are coded and sent

along the fibre as pulses of laser light.

An endoscope contains a long thin bundle of optical fibres. It is an

instrument used by surgeons for looking inside the body.

MiragesOn a very hot day, roads can get very hot. This will cause the air just above the

road to become hot and its density will therefore change. Rays coming from the

sun will be refracted by the cool and warm air and are incident at the hot air at an

angle greater than the critical angle so these rays are reflected completely and

we see a mirror image of whatever is on the road. This image is called a mirage.

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