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WEEK 1

REFLECTION OF LIGHT WAVES

Light is a form of energy which causes sensation of vision. It is an electromagnetic wave which travels through a vacuum. It is usually radiated outward from a source e.g sun.

Luminous Objects

Are the objects which give out light themselves? They are self-luminous objects. Natural examples of self-luminous objects are sun, stars, fire flies & glow worms. Artificial luminous objects are touch lights, candles, electric lamps e.t.c.

Non-luminous objects

Are the objects which do not produce their own light. They are seen when light from other sources fall on them and reflect back. For example, road signs, page of a book, the moon and a person’s face. The sun’s ray illuminate the moon which makes it appears luminous in the night.

Transparent objects

Are the objects which allow light ray to pass through them without absorbing them e.g glass, water, air.

Translucent Objects

Are objects which allow small amount of light ray to pass through them e.g Frosted glass, tissue paper.

Opaque Objects

Are the objects that do not allow light rays to pass through them e.g Brickwall, wood blackboard, cardboard e.t.c.

Rectilinear Propagation of light

This shows that light rays travels in a straight line. This can be shown using two card boards paper. One is folded straight while the other is bent.

A candle light is place at one end of each of the folded cardboard and each is viewed from the other end. It is observed that light from a straight cardboard is seen while light from the bent one is not seen.

This shows that light travels in a straight line.

Candle light

Candle light

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There are two natural effect which results from the rectilinear propagation of light these are

(i) Shadows (2) Eclipse

Shadows

Is formed by opaque objects. A shadow is the area to which light ray cannot reach because of the obstruction of an opaque object.

A small source of light produces a sharp shadow (umbra) while a large source of light produces a (sharp shadow (umbra) and a partial shadow (penumbra).

Eclipse

An eclipse occurs as a result of a shadow cast by one heavenly body on another.

Eclipse of the sun or solar eclipse

This occurs when the moon comes between the sun and the earth and the moon’s shape or shadow is cast upon the earth’s surface. For people in the umbra region, it is total darkness or eclipse while people in the penumbra region, it is partial darkness or partial eclipse.

Diagram

To be practice and draw from text book

Lunar eclipse or eclipse of the moon

This occurs within the earth is between the sun and the moon. The shadow of the earth is thrown on the moon.

To be draw from textbooks

Annular eclipse of the sun

This occurs when the sun and the moon are positioned sect before reaching the earth. The sun is covered leaving a bright ring of light around its edge.

To be draw drawn from text books

WEEK 2

PLANE MIRRORS

A plane mirror is produced by coating one side of the plane glass with silver. The silver coated surface prevents light ray from passing through the glass and does serve to reflect the light ray.

Images formed by plane mirrors

(a) Image at a point: The image of a point formed by plane mirror is

(i) as far behind the mirror as the point is in front of it.

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(ii) the line joining the point to its image is perpendicular to the mirror.

(b) Image of a whole object in front of a plane mirror is laterally inverted. This is shown clearly if a printed word such as “BEST” is held in front of a plane mirror.

ROTATION OF A MIRROR

When a plane mirror is rotated through an angle degree, the reflected ray will rotate through twice the angle provided the direction of the incident ray remains constant.

Suppose a beam of light OM is incident normally on the mirror at M. The beam is reflected straight back along MO to the point O. The incident ray OM and reflected ray after rotation is MP. If θ, then the reflected ray is rotated through 2θ.

Angle OMR = 2θ tan 2 θ =

Where d = OP and D = OM 20 = tan – 1

Angle of rotation, θ

=

Example 1

The reflection of a narrow beam of light incident normally on a plane mirror falls on a metre rule parallel to the mirror at a distance of 1.0m. Calculate the angle of rotation of the mirror if the reflected beam is displaced 21.26cm along the metre rule when the mirror is rotated.

D

M

20

d p o

θ θ

4

Let the angle of rotation of the mirror = 0 tan 2 =

tan 2 =

2 = tan – 1 0.2126 2 = 12.002 =

= 6.0010

Angle of rotation of the mirror = 60.

Images formed by two parallel mirrors

When an object is placed in between two parallel mirrors, the numbers of images formed is infinite ()

Images formed by two inclined mirrors

If two mirrors are inclined at an angle of to each other, the number of images formed,

n =

Uses of plane mirrors

Plane mirrors can be used;

1. As looking glass

2. In periscope for seeing round corners or over obstacles.

A simple periscope consists of two plane mirrors inclined at 450 and fixed facing each other.

1m D 20

d

26.26 0.2126m

Metre rule

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3. In kaleidoscope.

4. In sextants – a navigational instrument which employs the advantage of rotation of a mirror to locate the correct altitude of the sun.

5. By opticians to obtain actual distance for testing the eye.

6. In mirror galvanometer to measure very small current.

Location of an Image

To locate the position of an image, five optical pins are used. The object pin O is placed in front of the mirror. Two pin A and B are use to locate image of O by placing it in line with image I formed.

Another set of two pins C and D are placed in line with image of O seen. By extending the two lines AB and CD they are observed to meet at a point. This point is the image position. The distance of this point to the mirror is observed to be equal to the object distance to the mirror.

Where y = x

Angle of deviation of light at plane mirror surface

When a ray of light is incident on a plan mirror surface AB, the ray is reflected along OD.

450

450 Observer

I Image

B

D

A

y

x

O object

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The deviation of the incident light CO along OD shows that the angle of deviation from the incident path is equal to twice the glancing angle

i.e = 2

Example

A ray of light from a lamp is incident at an angle of 300 to the normal. If the image of the lamp is formed 10cm from the mirror.

Calculate (1) the distance between the lamp and its image

(2) the angle of deviation

Solution;

(1) The distance between the lamp and the mage = twice the image distance to the mirror. = 2 x 10cm = 20cm

(2) The glancing angle = 900–1 where i = angle of incidence = 900 – 300 = 600

Therefore, angle of deviation = 2 = glancing angle = 2 x 600 = 1200

REFLECTION BY CURVED or SPHERICAL MIRRORS

There are two types of curved mirrors.

D

i r

A B

C

ε

O δ = angle of deviation

Normal (N)

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1. Concave or converging mirror

2. Convex or diverging mirror

Concave Mirror

This is a type of spherical mirror in which the reflecting surface bends inwards. It causes rays of light to converge after reflection.

Convex Mirror

Is a type of curved mirror in which the reflecting surface bends outwards. It causes rays of light to diverge after reflection from the mirror.

Basic terms and definition

1. Principal axis

This is the line from the pole p to the centre of curvature c.

2. Aperture (CD).

Is the width or thickness of the mirror.

3. Pole, (P)

Is the centre of the mirror.

4. Centre of curvature, (c)

Is the centre of the sphere in which the mirror is a part.

5. Radius of curvature (r)

Is the distance between the pole and the centre of curvature.

6. Principal focus (f)

Is the point in the principal axis to which all parallel rays of light converge (as in case of concave mirror) or appear to diverge (as in case of convex mirror) after reflection from the mirror.

7. Focal length (f)

Is the distance between the pole and the principal focus. The focal length is half the radius of curvature.

i.e F =

C

D

r

C f p

C

r

C f

D

p

Concave mirror Convex mirror

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HEMISPHERICAL MIRROR

These are the mirror with large aperture. When wide parallel rays of light not close to the principal axis are incident on it, they are observed to converge of different points on the principal axis. The reflected rays before reaching the principal axis intersect to form a brightly luminated curved surface called caustic curve.

SPHERICAL ABERRATION

Is a type of defect in curved mirrors of wide aperture. It is a defect arising when wide parallel rays are brought into focus at different points on the principal axis. The defect can be corrected by ensuring that the mirror is of small aperture compared with the radius of curvature.

PARABOLIC MIRROR

This is also called reflecting surfaces are used to reflect parallel rays of light from the principal focus without loss of intercity considering the size of the aperture. Such reflecting surfaces are used in ear headlamps.

Parabolic mirror

IMAGES FORMED BY A CONCAVE MIRROR

To be discussed in class

APPLICATION OF CURVED MIRRORS

1. Used as looking mirrors i.e when a man places his face near the curved mirror, an enlarged, erect, virtual image is formed.

2. As a reflector in a reflecting telescope and microscope.

3. As a driving mirror convex mirror gives a wide field of view and also gives upright image of the object.

4. A parabolic mirror used in car headlamps and searchlight.

Caustic curve

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MIRROR FORMULA

If V = image distance from pole u = object distance from pole f = focal length =

The mirror formula is = +

GRAPHICAL REPRESENTATION OF FORMULA

If a graph of is plotted against for different position of object with corresponding image distance, the graph obtained is a straight line graph with intercept at both axes equal to the reciprocal of the focal length.

Example

If the intercept of axis is 0.05 from the graph of against , determined the

focal length of the concave mirror used.

Solution

Intercept on either axis =

0.05 =

f =

= 20cm

Magnification of curved mirror

Is the ratio of the image distance (or height) to the object distance (or height).

i.e Magnification = –

10

Magnification, m = V = Image distance (or height) u = Object distance (or height)

Note: Magnification can also be obtained using mirror equation.

Assuming equation of mirror is multiplied by v, then *

= magnification

Note: Graph of m (magnification) against v (image distance) gives a straight line with intercept on the m axis of m = 1.

Sign Convections

This is of great importance in order to distinguish between image positions when they are formed in front of a curved mirror or sometimes behind it. With this in mind it will be easy to obtain correctly the image positions by calculation using the mirror equation ( = +

). The two commonly used sign conventions are

(1) Real is positive

(2) New Cartesian

Real is positive New Cartesian

1. Real object and real image are considered to be at a positive distance from the mirror

Distances measured to the right of the mirror are positive.

2. Virtual images are at a negative distance from the mirror.

Distances measured to the left of the mirror are negative.

3. Focal length of a concave mirror is positive

Focal length of a mirror is negative

4. Focal length of a convex mirror is negative.

Focal length of a convex mirror is positive.

– 1

V

M

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Example

An object is placed 10cm in front of curvature 12cm. Calculate the position, nature and magnification of image formed. r = 2f = f

f = = 6cm

Using mirror formula

= +

= +

+

=

=

= 30

V = = 15.0cm

Magnification, M =

=

= 1.5cm

Example

An object is placed 15cm in front of a convex mirror of focal length 10cm. Calculate the image distance and the magnification produced.

Solution

Object distance u = 15cm Focal length, f = –10cm. (the negative sign implies that the convex mirror has a virtual focus). Let the image distance = V Using mirror equation

= +

= +

12

– =

=

=

5v = 30

V =

V = –6cm This shows that the image formed is virtual and in front of the principal focus. Magnification, m =

=

= 0.4

WEEK 3

REFRACTION OF LIGHT (Cont’d)

Refraction through a prism Case 1:

For a ray of light incident at an angle i to the normal along face AB of the glass prism emerge at the face AC after refraction at the two faces.

e0 = emergency angle N = normal A = refracting angle

D0 = minimum deviation i = incidence angle ro = refracted angle

Generally; rays passes symmetrically through the prism. The refracted ray in glass is parallel to the base BC and the emergent ray bend towards the base. The angle of deviation,

D = 2i – 2r

>

A

eo D

or

A

i

Ao

B C

Incident ray

Emergent ray

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and refracting angle of the prism A0 = 2r

Then D = 2i – A D + A = 2i i =

Since refracting angle of the glass prism Ao = 2r0 refracted angle r0 =

From Snell’s law n =

substituting for i and r

n =

Case 2: For incident ray parallel to the base of the prism. The ray passes symmetrically through the prism and the refracted ray in glass is not parallel to the prism.

i0 = angle of incident r0 = angle of refraction e0 = emergent angle

REFLECTIONOF PRISM

Case 1 Using a glass prism with angles of 900, 450 and 450 (i.e Isosceles prism). A ray of light incident normally at the side BC passes normally at the side BC passes through it and strike the hypotenuse BA at an angle of 450. As this angle greater than the critical angle for glass i.e C = 420, the r ay becomes totally reflected with an angle of reflection 450. The reflected ray strikes the glass of face AC and thus passes through the prism.

Emergent ray

i

A

C B

Incident ray 0r

e0

> 450

450

Incident ray

reflected ray

emergent ray

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Turning ray of light through 1800

Advantages of Prisms 1. Used in prism periscope to produce a high quality image then plane mirrors

which give multiple images due to multiple reflection of light ray. 2. They do not tarnish or deteriorate as mirrors. 3. Used in prism binocular.

ELECROMAGNETIC WAVES Electromagnetic spectrum consists of the following series of radiation which include radio waves, microwaves, infra red, visible light, ultra violet, x-rays gamma ray. The spectrum is given in the table below in order of their decreasing wavelength and production method.

Type of radiation Wavelength λ

Method of Production

Method of detection

1. Radio waves 104m Through radio transmitter

T. V. receivers

2. Micro waves 10– 1 m Same as above Same as above 3. Infra red 10– 4 m - 10– 5 m Warm objects Thermopile 4. Visible light 8 x 10– 3m to 3 x

10– 7m Hot sources The eye

5. Ultra violet 10– 7m to 10– 5m Very hot sources

Fluorescent substances, photocells

6. X-ray

10– 8m to 10– 12m

Bombardment of a metal target by high speed electrons

Geiger-counter

7. Gamma ray (α) 10– 10m to 10– 14m Nuclear reactions

Photographic plate of film or Geiger–Muller detector

> >

< <

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CRITICAL ANGLE Is the angle of incidence in the denser medium when the angle of reflection in the less dense medium is 900.

TOTAL INTERNAL REFLECTION OF LIGHT

Is the reflection of an incident ray of light at the interface between the medium of incidence and another medium of lower refractive index when the angle of incidence in the denser medium exceeds the critical angle.

CONDITIIONS FOR TOTAL INTERNAL REFLECTION OF LIGHT TO OCCUR 1. The light must be travelling from an optically more densed medium to an

optically less dense medium. 2. The angle of incidence in the denser medium must be greater than the critical

angle. (a)

i < c i.e incident angle < critical angle (b)

i = c i.e angle of incidence = critical angle

>

critical angle

refracted ray (900)

incident ray

glass air

strong refracted ray

weak reflected ray

i

r

Incident ray

Glass air

strong refracted ray

weak reflected ray

c Glass air >

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(c)

i > c (critical angle is exceeded there is total internal reflection).

When the angle of incidence is greater than the critical angle

Relationship between critical angle and the refractive index

At critical angle c, the angle of refraction is 900. For light ray travelling from glass to air medium from Snell’s law,

gna = =

angle of refraction = 900 at critical angle C. then gna =

Similarly, refractive index of light travelling from air to glass ang =

ang, =

Sin 900 = 1

ang =

Sin C =

the critical angle c, is obtained as C = Sin– 1

Example The refractive indices of glass and water are 1.5 and 1.3 respectively, what will be the critical angle when the angle of refraction in the water medium is 900? Solution

Refractive index of glass =

refractive index of water

=

Since sin 900 = 1

strongly reflected ray (total internal reflection)

Glass air

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1.5 x Sin c = 1.3 x 1 sin c =

Sin c = 0.86667 C = Sin– 1 0.86667 Critical angle, C = 600

Example Find the critical angle for light travelling from water to air (take n = )

Solution n =

=

4 sin c = 3 Sin c =

Sin c = 0.75 c = Sin– C 0.75 c = 48.590

APPLICATION OF TOTAL INTERNAL REFLECTION 1. Information of mirage

Mirage: A phenomenon which occurs as a result of progressive bending of light ray as it crosses the region of warmer layer of air of decreasing refractive index until it becomes parallel to the ground after which it proceeds to bend upward.

2. In fish-eye view.

It enables a fish to have full view of everything above the water at any depth provided the surface of the water is not ruffled. A fish has 1800 field of view which is squeezed into a cone of about 980 which is twice the critical angle of water.

3. In prismatic binocular and periscope

To see over barriers and round corners and produce high quality and sharp image better than plane mirror which produces multiple image.

4. In optical fibre - to see deep down the throat of a patient. - use to convey information in T. V. channels or telephone conversation

line .

cool air

Pool of water

sun ray

I

Warm air

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WEEK 4 LENSES

A lens is a piece of glass which is curved on both sides. Types of lens

There are two main types of lens.

1. Convex (or converging) lens 2. Concave (or diverging) lens This is a type of lens that have its centre thicker than its ends. The thickness at the centre makes the lens surface to curve outward. Convex lens causes close parallel rays of light to converge at a point after refraction.

Concave lens A concave lens has the centre thinner than its ends. This makes the lens surface to curve inwards. This causes close parallel rays of light to diverge after refraction.

Types of convex lens

> >

> >

+ f

Convex lens Parallel rays

>

>

Bi – convex lens Plano Convex

Convex meniscus

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Types of Concave lens

Uses of a lens 1. To correct eye defect 2. In camera to take picture

3. In microscope to magnifying microscopic object 4. In projection lantern to bring to focus image of object 5. In compound microscope to see distant object

Image formed by concave and convex lenses To be discussed in class with solved questions

DISPERSION OF WHITE LIGHT

Is the separation of white light into its components colours of RED, ORANGE, YELLOW, GREEN, BLUE, INDIGO and VIOLET notably called ROYGBIV. The reason for this is because different light (colour) travels at different speed through glass. The most deviated light is VIOLET while the least deviated light is RED.

However, if another identical prism is placed to intercept the refracted ray, a wider spectrum of light is observed.

On the contrary, if the second prism is inverted, the colours are seen to disappear and only a patch of white light is seen.

Bi-concave lens Plano concave lens Concave meniscus

ROYGBIV

Incident white light

Prism Screen

> >

> Incident white light

a pitch of white light

screen

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FORMATION OF PURE SPECTRUM In formation of a pure spectrum two converging lenses and a prism arranged as givenin the diagram.

MONOCHROMETER

This is the light of the wavelength which passes through a prism refraction occurs without dispersion. A monochromatic light of yellow colour is obtained from a sodium light.

PRIMARY AND SECONDARY COLOURS There are 3 main primary colours. These are RED, BLUE and GREEN. They cannot be made by any combination of the three primary colours. However, the combination of the three primary colours give a white light.

Secondary Colours Are the colours obtained by mixing any two of the primary colours e.g Red + Green = Yellow

Green + Blue = Cyan Red + Blue = Magenta The addition of primary colours to produce other colour is known as addition of colour. A necessary way of remembering addition of colour is by using colour triangle or Venn diagram.

>

> > >

> >

> >

> >

> > slit

f

Collimator

prism f

Telescope

Violet

Red

Converging lens

yellow

Green

Red

Blue

Magenta

Cyan Colour triangle

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White light is produced when secondary colour is mixed with the colour directly opposite to it in the colour triangle. Green + Magenta = white light

Blue + Yellow = white light Red + Cyan = white light The two colours added as shown in the example above is called a complementary colours.

Colour Filter

This allows light of one colour to pass through it while absorbing light of other colours. The filter made of red colour while absorbing other colours except red. Also, if the filter is green, it will absorbing other colours except green

THE HUMAN EYE

Green

Cyan Blue

Magenta

Red Yellow

White

Red

Green

Blue

Red

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The essential parts of the human eye include 1. The Cornea

A thick transparent bulge in the front part of the eye. It serves as a protective covering in front of the lens and it allows light into the eye. It also partly focus the light entering the eye.

Aqueous humour It is the transparent part between the cornea and the lens. It allows light to pass through it. Vitreous humour. It is a jelly-like liquid between the lens and the eye ball. These liquid serves mainly to keep the eye in its spherical shape. The Iris It is behind the cornea. The Iris is the part which gives the colour of the eye. It acts as a stop or a diaphragm of variable size. It has a tiny opening at the centre called pupils. The iris adjusts the amount of light entering into the eye. Pupils Is the black hole in the centre of the iris through which the light passes.

A Crystalline lens This focuses the light entering the eye on the sensitive retina. The Ciliary muscles These support the lens and attach it to the wall of the eye. These ciliary muscles by their expansion and contraction alter the focal length of the lens changing its shape. Retina It is the light sensitive area of cells at the back of the eye. These images are formed on the retina which consists of light sensitive nerve connected to the optic nerve. The optic nerve conveys the sensation of sight to the brain. Yellow Spot Is the most sensitive part on the retina. It is part where light entering the eye are usually brought to focus and image is formed.

Blind Spot This is the spot on the optic nerve from the retina. It is insensitive to light. Sclerotic layer It is the outer covering of the eye.

(1) Cornea is responsible for the refraction of light entering into the eye. (2) It has a refractive power twice that of the eye lens.

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(3) Aqueous and vitreous humour maintains the shape of eye ball. Accommodation

Is the ability of the eye to alter or adjust the focal length of its lens so as to form a clear image of object at different distance on the retina. The adjustment is brought about through the action of the ciliary muscle.

A CAMERA A camera consists of a converging lens, a sensitive film in a light box. A diaphragm which controls the amount of light admitted through the lens and a shutter of variable speed which opens to take the photograph. The photographic lens is moveable so that the distance between the lens and the film can be varied.

Persistence of Vision

This is the ability of the brain to retain the impression of an image formed on th retina for a time after which the light energy is removed.

Binocular Vision

This is the over lapping of the two images formed by both eyes which give an impression of depth and solidity and makes it possible to see object in relief such a proper prospective of an object is impossible with one eye.

Near Point

Near point of a normal eye is the nearest distance of distinct vision. The least distance of an object to the eye is 25cm.

Fear point The far point of a normal eye is the farthest distance of distinct vision and it is at infinity.

Len’ defect 1. Chromatic aberration

In a simple lens defects, this occur due to formation of coloured images. It can be corrected by using a suitable lens of different material beside a converging lens to form achromatic doublet.

Spherical aberration

Bi-concave lens made of flint glass Bi-convex lens of

crown glass

Achromatic doublet

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This defect occurs when parallel rays of light are brought into focus at different points on the principal axis. This can be corrected by

1. Surrounding the lens with opaque disk having a hole in the middle so that narrow beam of light can be allowed through it. This method reduces the brightness of the image formed.

2. Using two planes convex lens at a distance equal to the average of their focal length.