CHAPTER FOURTEEN: BEHAVIOUR OF LIGHT – PHYSICS S1-S2 NOTES

14.1 INTRODUCTION

Optics is a branch of physical science dealing with the propagation and behavior of light.

Light is a form of energy that travels in a straight line.

(a) Rays and Beams of Light

(i) Rays: A ray is the direction of the path taken by light.

Diagrammatically, it is represented by a straight line with an arrow.

(ii) Beam: A beam is a stream of light energy.

It is represented by a number of rays.

(b) Types of Beams

There are three types of beams, namely:

• Parallel beam,
• Convergent beam, and
• Divergent beam.

Diagrams showing the three types of beams

14.11 Rectilinear Propagation of Light

The rectilinear propagation of light states that: Light travels in a straight line.

Experiment 14.1 To verify the rectilinear propagation of light

Apparatus:

Source of light, three slits, screen, retort stand.

Procedure:

• Stand the slits such that they are in a straight line.
• Place the source of light at one end such that it is at the same level with the three holes.
• View the source of light from the other end as shown in figure 14.1 below.

Figure 14.1

Result: The source of the light can be seen.

Procedure continued

• Now displace any one of the slits such that the holes are not in a straight line.
• Observe the source of the light as before.

Result: The source of the light can no longer be seen.

Explanation: Since the holes are no longer in a straight line, the light ray strikes the surface of the displaced slit.

Conclusion: Light travels in a straight line.

14.12 Applications of the Rectilinear Propagation of Light

The rectilinear propagation of light is applied in:

• Shadows
• Eclipses
• Pinhole camera

(a) Shadows

A shadow is a dark area caused by an opaque object blocking a ray or a beam of light. A shadow may be described as umbra and penumbra.

(i) Umbra:

The fully shaded inner region of shadow cast by an opaque object, especially the area on the earth or moon experiencing totality in an eclipse.

In the laboratory, it may be obtained when a point source of light is enclosed in a box with a very small hole on one of its sides and an opaque object is placed between the source of light and a screen as shown in figure 14.2.

A diagram showing the formation of umbra using a point source of light

(ii) Penumbra: The partially shaded outer region of the shadow cast by an opaque object, especially the area on the earth or moon experiencing partial eclipse.

It can be obtained when a source of light is enclosed in a box with an extended or larger hole on one of its sides and an opaque object is placed between the source of light and a screen as shown in figure 14.3 below.

A diagram showing the formation of penumbra using an extended source of light

(b) Eclipses

Eclipse, in astronomy, is the obscuring or blocking of light from the sun by a celestial body (e.g., the moon or the earth).

14.13 Types of Eclipse

Two kinds of eclipses involve the earth. These are:

(i) Solar eclipse and

(ii) Lunar eclipse

1. Solar eclipse

   A solar eclipse occurs when the moon is between the sun and the earth and its shadow moves across the face of the earth.

Solar Eclipse is divided into two, namely:

(i) Total solar eclipse and

1. Annular eclipse

Total solar eclipses

Total solar eclipse occurs when the moon’s umbra reaches the earth as shown in figure 14.4 below.

(ii) Annular eclipse (Partial Eclipse)

The Moon’s orbit around Earth is slightly elliptical, or egg-shaped. Therefore, the distance between Earth and the Moon varies slightly as the Moon orbits Earth. When the moon is farther from Earth than usual, it appears smaller and may not cover the entire sun during an eclipse. A cone of umbra forms in the upper atmosphere and does not reach the earth’s surface. As a result, the whole area on the earth’s surface is covered by penumbra. See figure 14.5 below. This type of eclipse is called an annular eclipse.

Off to the sides of the path of a total eclipse, a partial eclipse, in which the sun is only partly covered, is visible. As such, a bright ring of the solar disk appears around the black disk of the moon.

At the beginning of a total eclipse, the moon begins to move across the solar disk about 1 hour before totality.

Notes:

• In areas outside the band swept by the moon’s umbra but within the penumbra, the sun is only partly obscured, and a partial eclipse occurs.
• The illumination from the sun gradually decreases and during totality (and near totality) declines to the intensity of bright moonlight.
• A total solar eclipse occurs about every 18 months.

(b) Lunar Eclipse (Partial or total obscuring of the moon by the earth’s shadow)

A lunar eclipse occurs when the earth is between the sun and the moon and its shadow is cast on the surface of the moon.

The earth, lit by the sun, casts a long, conical shadow called umbra in space. At any point within that cone the light of the sun is wholly obscured. Surrounding the shadow cone is an area of partial shadow called the penumbra. See figure 14.6 below.

Lunar Eclipse is divided into two types, namely:

• Partial lunar eclipse and
• Total lunar eclipse.

(i) Partial lunar eclipse

A partial lunar eclipse occurs when only a part of the moon enters the umbra and is obscured. This is the case when the moon is in position P3. Figure 14.1.

(ii) Total lunar eclipse

A total lunar eclipse occurs when the moon passes completely into the earth’s umbra. That is when the moon is in position P2, figure 14.1. In positions P1 and P4 there is no eclipse, but the moon is less bright.

Notes:

• Before the moon enters the umbra in either total or partial eclipse, it is within the penumbra and the surface becomes visibly darker.
• The portion that enters the umbra seems almost black, but during a total eclipse, the lunar disk is not completely dark; it is faintly illuminated with a red light refracted by the earth’s atmosphere, which filters out the blue rays.
• Occasionally a lunar eclipse occurs when the earth is covered with a heavy layer of clouds that prevent light refraction; the surface of the moon is invisible during totality.

14.14 The Pinhole Camera

(a) Structure

A pinhole camera is made of a light-proof box painted black on the inside with a small pinhole in front and a piece of frosted glass or tracing paper placed at the back as the screen.

(b) Mechanism

An illuminated object is placed in front of the camera. Light rays from the object pass through the pinhole and form an inverted, backwards image of the subject on the screen at the back of the box.

A diagram showing the formation of image in a pinhole camera

A photograph of a dog formed in a pinhole camera

(c) The Nature of the Image formed by a Pinhole Camera

The nature of the image formed by a pinhole camera is described by using the following terms.

(i) Real – Formed by intersection of actual rays and can be obtained on screen.

1. Inverted – Upside down
2. Diminished – Smaller than the object
3. Magnified – Bigger/larger than the object.

(d) The effect of the object distance on the size of the image

The size of the image, magnified or diminished, depends on the object distance.

1. When the object distance is small

When the object is moved towards the pinhole or when the camera is moved towards the object, such that the object distance is small, the image becomes magnified.

1. When the object distance is large

When the object is moved away from the pinhole, or when the camera is moved away from the object, such that the object distance is large, the image becomes diminished.

(e) The effect of the size of the pinhole on the nature of the image formed in a pinhole camera

When the pinhole is small, the image is sharp or clear and is said to be in focus. But when the hole is bigger, the image is blurred (brighter).

Explanation

The blurred image is explained by the fact that a large hole is believed to be made up of a collection of many small holes, each of which produces an image slightly displaced from the other images. The result is thus a brighter (blurred) image.

(f) Magnification, m, of the pinhole camera

Magnification, m, is the ratio of the image height to the object height.

Consider the cross section of the pinhole camera

Magnification = =

m =

Or Magnification =

m =

From the above equations, we have

=

=

Or Magnification =

m =

Example

1. An object of height 5 cm is placed 20 cm from a pinhole camera which is 5 cm long. If the height of the image formed is 1.25 cm, calculate the magnification.

Solution: u = 20 cm, v = 5 cm (length of the camera), Oh = 5 cm, Ih = 1.25 cm, m = ?

Magnification = = = = 0.25

Or Magnification = = = = 0.25

2. A man 1.75 m tall stands at a distance of 7.0 m from the pinhole of a pinhole camera. If the film is 0.20 m behind the pinhole, find the length of the image of the man formed on the film.

A. 8.75 m B. 4.00 m C. 0.80 m D. 0.05 m

Solution: h_o = 1.75 m, u = 7.0 m, v = 0.20 m, h_i = ?

Using = Þ = h_i = = 0.05 m. Therefore the answer is D.

Self-Check 14.1

1. When a pinhole camera is moved nearer an object, the size of the image

A. remains the same B. becomes smaller

C. becomes larger D. becomes diminished

2. In a pinhole camera, sharper and taller images are obtained by

A. widening the hole and moving the object farther

B. narrowing the hole and moving the object nearer

C. using a longer camera with a wider hole

D. using a shorter camera with a narrower hole

3. (a) Describe an experiment to show that light travels in a straight line.

(b) With the aid of a diagram, illustrate how the shadows are formed when an opaque object is placed between an extended source of light and a screen.

4. (a) An object of height 4 cm is placed 5 cm away from a pinhole camera. The screen is 7 cm from the pinhole.

(i) Draw a scale ray diagram to show the formation of an image by a pinhole camera.

(ii) What’s the nature of the image.

(iii) Find the magnification.

(iv) Explain what happens to the image if the pinhole is made larger.

1. Draw diagrams to show the formation of a partial and total solar eclipse.

REFLECTION OF LIGHT

14.2 Reflection

Definition: Reflection is the change in the direction of a light ray or a beam of light after impinging on a surface.

(a) Types of reflecting surfaces

Reflection occurs on two types of reflecting surfaces, namely:

(i) Plane surface e.g., plane mirrors.

(ii) Curved surfaces e.g., curved mirrors.

(b) Reflection on plane surfaces

Terms used

The figure 14.21 below illustrates the terms used in the study of reflection of light.

Figure 14.21

MM’ – represents the plane mirror.

PO – Incident ray is the ray of light falling on the reflecting surface.

OQ – Reflected ray is the ray of light that leaves the reflecting surface after reflection.

ON (Normal) – is a perpendicular line that meets the reflecting surface.

Point O – Point of incidence is the point on the reflecting surface where the incident ray, the reflected ray, and the normal all meet.

∠PON = Angle of incidence – is the angle made by incident ray and the normal.

∠NOQ = Angle of reflection – is the angle made by the normal and the reflected ray.

∠MOP = ∠M’OP = Glancing angle, g: – is the angle between the incident ray or reflected ray and the reflecting surface.

∠ROQ Angle of deviation, d.

The angle of deviation is the angle between the reflected ray and the original path of the incident ray.

14.22 Types of reflection

There are two types of reflection, namely:

1. Regular Reflection
2. Diffuse (Irregular) reflection

(a) Regular Reflection

Regular reflection is the type of reflection in which a parallel beam is reflected parallel.

It occurs on smooth reflecting surfaces and gives clear images of objects, thus allowing them to be recognized.

(b) Diffuse (Irregular) reflection

Diffuse or Irregular Reflection is the type of reflection in which a parallel beam is scattered after reflection.

It occurs on rough reflecting surfaces. Because the reflected beam is scattered after reflection, it does not form clear images of objects.

Difference between Regular and Diffuse Reflections

Note: 1. Not all of the light that strikes a mirror is reflected; some of it is absorbed by the reflecting object and the object becomes warmer.

2. The laws of reflection are obeyed for each ray.

14.23 The Laws of Reflection

The reflection of light from a reflecting surface is governed by two laws. These laws are called laws of reflection. They are stated as follows:

LAW 1 The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.

LAW 2 The angle of incidence is equal to the angle of reflection.

The situation is illustrated in the figure below.

Where: i = Angle of incidence, r = Angle of reflection

According to law 1, point of incidence, O, which lies in the plane formed by the reflecting surface, is a common point for the incident ray, the reflected ray, and the normal. That is to say, all three lie in the same plane.

Law 2 is about the angles made by the incident ray and the reflected ray with the normal. That is ∠i = ∠r. However, the laws of reflection can be verified experimentally.

Experiment 14.1 To verify the laws of reflection

Apparatus: A strip of a plane mirror, 4 optical pins, 4 office pins, a white piece of paper, and drawing board.

Procedure

• Fix the white sheet of paper on the drawing board using the office pins.
• Draw a straight thin pencil line MM’ as shown in figure 14.23.
• Stand a strip of a plane mirror up vertically, with the silvered surface on the line MM’ drawn on the paper.
• Fix object pin O, in front of the mirror about 10 cm from line MM’.
• View the image, I, of the object, O, by placing your eye at position E₁ and fix two pins P₁ and P₂ such that they are collinear (on a straight line) with I.
• Remove the two pins P₁ and P₂.
• Repeat the above procedure with the eye in position E₂.
• Remove the mirror.
• Join the points P₁, P₂, P₃, and P₄ to meet MM’ at B₁ and B₂.
• Extrapolate the lines to intersect at I.
• Construct the normals, B₁N₁ and B₂N₂.
• Measure the angles i₁ and r₁, i₂, and r₂.

Results: 1. The incident rays (OB₁ and OB₂), the reflected rays (B₁E₁ and B₂E₂), and the normals N₁ and N₂ at the points of incidence B₁ and B₂ all lie in the same plane.

2. The angle of incidence, i₁ = Angle of reflection r₁ and the angle of incidence, i₂ = Angle of reflection r₂.

Conclusion: The laws of reflection are verified.

(a) Image Formation by Plane Mirrors

The formation of an image by a plane mirror is illustrated in figure 14.24 below.

Rays of light from a real object O are reflected by the mirror and enter the eye in such a way that they appear to have come from I. It follows that the image of the object is at I. Since the rays appear to have come from I, the image is a virtual image.

(b) To show that the Line Joining a Point Object and its Image is Perpendicular to the Mirror

Consider the diagram in figure 14.25 below in which I is the image of point object O, and ON is perpendicular to the mirror.

It follows from the second law of reflection that a ray incident along OM must be reflected back along MO. Since this reflected ray appears to have come from the image, I, it follows that OMI are collinear (i.e., are on a straight line) and therefore, OI is perpendicular to the mirror. That is to say, the line joining object and image is perpendicular to the mirror (reflecting surface). Also by measurement, OM = MI. This shows that the image is as far behind the mirror as the object is in front of it.

(c) Image Location by No-parallax

The method of no-parallax is used in light experiments to locate the images of objects formed in a mirror.

In this method, the eye is moved from side to side while viewing a search pin until a position is found for which both the object pin and the image appear to coincide in the same straight line.

(d) Rotation of a Plane Mirror

Consider the diagram below in which a plane mirror M₁M₁‘ is rotated through an angle.

M₁M₁‘ = Position of mirror before rotation

M₂M₂‘ = Position of mirror after rotation

Angle, θ = Angle of rotation of the mirror

= ∠M₁OM₂ = ∠M₁‘OM₂‘

When a plane mirror is rotated through an angle, θ, while keeping the direction of the incident ray along the same path, it can be proved that:

=

I.e. The angle of rotation of the reflected ray = 2θ

Derivation of the formula

The incident ray, AO, makes an angle, i, with the normal. The angle between the angle of incidence and the angle of reflection, AOB

= AON + NOB

= i + r But by the second law of reflection i = r

= i + i

= 2i …………………… 1

If the mirror is rotated through an angle, θ, the normal must also turn through the same angle of rotation, θ. This gives a new angle of incidence (i + θ).

But by the second law of reflection, the angle of incidence = angle of reflection.

Therefore, the reflected ray has also turned through an angle (i + θ).

Hence, the new angle between the angle of incidence and the angle of reflection

= Angle of incidence + Angle of reflection

= (i + θ) + (i + θ)

= i + θ + i + θ

= 2i + 2θ …………… 2

As the incident ray remains in the same path, the angle of rotation of the reflected ray is given by the formula:

= –

= Equation (2) – Equation (1)

= 2i + 2θ – 2i

= 2θ

Thus when a mirror is rotated through an angle, θ, the angle of rotation of the reflected ray = twice the angle of rotation of the mirror.

(e) Properties (Characteristics) of Images formed in Plane Mirrors

The image formed in a plane mirror has the following properties.

1. The image is the same size as the object.
2. The image is as far behind the mirror as the object is in front.
3. The image is laterally inverted. See figure 14.28 below.
4. The image is virtual (cannot be obtained on film) for a real object.

Figure 14.28

(f) Formation of a Real Image from a Virtual Object by a Plane Mirror

We have seen that a plane mirror produces a virtual image of a real object. It follows from the principle of reversibility of light that a plane mirror must produce a real image of a virtual object as shown in figure 14.29.

(g) The Number of Images formed by Two Mirrors Inclined at an Angle θ

When an object is placed between two mirrors inclined at an angle, θ, a number, n, of images is formed. The value of n is calculated from the formula:

n = – 1

Examples

Find the number of images of an object placed between two mirrors inclined at:

(a) 90° (b) 60° (c) 45° (d) 0°

Solution

(a) θ = 90°, n = ?

(b) θ = 60°, n = ?

Using n = – 1

= – 1

= 4 – 1 = 3

n = 3

n = 5

(c) θ = 45°, n = ?

(d) θ = 0°, n = ?

n = – 1

n = – 1

= 8 – 1 = 7

n = 7

n = ∞

Formation of Image when the angle of Inclination is zero (i.e. θ = 0)

14.24 Applications of Reflection in Plane Mirrors

Reflection in plane mirrors is applied in the following:

1. Periscope
2. Kaleidoscope
3. Salons and dressing rooms for admiration
4. Small vehicles by drivers to see the activities of passengers aboard
5. Bicycles for seeing traffic behind

(a) Periscope

An optical instrument for conducting observations from a concealed or protected position.

(i) Structure

A simple periscope consists essentially of reflecting mirrors at opposite ends of a tube with the reflecting surfaces parallel to each other, and at a 45° angle to the axis of the tube.

(ii) Mechanism

A ray of light from an object is successively reflected by the two mirrors inclined at 45° so that the image of an object on the other side of an obstacle is seen by an observer. See figure 14.31 below.

Periscopes are commonly used in:

• National theatres,
• Football pitches, and
• Submarines

Notes: The modern submarine periscope is a larger and more complex instrument. It consists of reflecting prisms at the top and bottom of the vertical periscope tube, with two telescopes and several lenses between them, and an eyepiece at the lower end.

Figure 14.32 shows a photograph of a cross section of a submarine periscope

(b) Kaleidoscope

An optical device that uses mirrors and objects to create a variety of colorful patterns.

(i) Structure

The kaleidoscope consists of three mirrors inclined at 60 degrees to each other and is fixed inside a light-proof tube with a small hole at one end. At the bottom of the tube is a ground glass plate to admit light into the tube.

(ii) How it works

Beads, colored glass, pieces of plastic, or mixtures of oil and water contained loosely between two glass or plastic disks are placed at the bottom of the kaleidoscope. Light enters the tube through the translucent glass or plastic, reflecting the images of the mirrors inside the tube giving multiple symmetrical images of objects inside the tube. When the tube is rotated, the tumbling motion of the items inside the compartment changes the patterns seen through the eyepiece.

Self-Check 14.2

1. Light energy is reflected when

A. angle of incidence is greater than angle of reflection

B. angle of incidence is equal to angle of refraction

C. angle of incidence is equal to angle of reflection

D. the normal at the point of incidence makes the same angle as the incident ray.

2. When reflection occurs in a plane mirror

(i) the image is real, erect and magnified

(ii) the angle of reflection is equal to the angle of incidence

(iii) the incident ray and reflected ray lie in different planes

(iv) the object and the image are at the same distance from the mirror

A. (i), (ii) and (iii) only B. (ii) and (iv) only

C. (i), (ii) and (iv) only D. (iv) only

3. An object is placed 30 cm in front of a plane mirror. If the mirror is moved a distance of 6 cm towards the object, find the distance between the object and its image.

A. 24 cm B. 36 cm C. 48 cm D. 60 cm

4. Objects P and Q are placed at distances of 2 m and 3 m respectively from a plane mirror as shown in figure 14.1. Find how far the image of P is from Q.

5. A person observes the image of a pin placed in front of a plane mirror as shown in figure 14.2 below. The reflected beam from the pin reaching the observer is a

SECTION B

6. (a) With the aid of diagrams, distinguish between diffuse and regular reflection.

(b) (i) State the laws of reflection.

(ii) Describe an experiment to verify the laws of reflection of light.

7. (a) State the applications of reflection in plane mirrors.

(b) Describe the structure and the mechanism of the periscope.