Light Wave – SS2 Physics Lesson Note (Second Term)

Light is a form of energy that travels as a wave motion. It has a very short wavelength of about 5×10^-4 mm and travels at 3.0×10⁸ m s^-1. Light comes from natural and artificial sources and travels in straight lines. Mirrors reflect it to form images.

Behavioural objectives

By the end of the lesson, students should be able to:

• state the sources of light and tell luminous from non-luminous objects;
• explain rectilinear propagation of light and how shadows and eclipses form;
• describe how a pinhole camera works;
• state the laws of reflection and describe the images formed by plane mirrors;
• describe the images formed by concave and convex mirrors;
• use the mirror formula and the magnification formula to solve problems.

What are the sources of light?

There are various sources of light: natural and artificial, luminous and non-luminous.

Natural sources of light include the sun and the stars. Artificial sources of light are candles, electric torches, electric lamps, incandescent lamps, arc lights and fluorescent lights.

Self-luminous or luminous sources of light are those that generate and emit light by themselves, e.g. the sun, stars, fireflies and some deep-sea fishes.

Non-luminous objects are seen when they reflect or throw back light from luminous objects. Examples of non-luminous objects are the moon, paper, mirror and wall.

When light falls on such a surface, it may be absorbed, transmitted or reflected. Sometimes a combination of these processes may occur.

What are light rays and beams?

A ray is the direction of the path in which light is travelling. It is represented by a straight line with an arrowhead.

———->———-

A beam is a collection of two or more rays of light. Beams can be parallel, convergent or divergent.

A parallel beam is made up of two or more rays travelling in the same direction that can never intersect each other.

————>———–
————>———–
————>———–

A beam of light is said to be convergent when the rays meet at a point.

A divergent beam is a collection of light rays that have the same source and spread out apart.

What is rectilinear propagation of light?

The phenomenon of light travelling in a straight line is known as rectilinear propagation of light.

It can be demonstrated by placing a candle flame at the end of a straight pipe. The light of the flame will be seen clearly at the other end of the pipe. If the pipe is then bent and the process repeated, nothing will be seen at the other end. This shows that light travels in a straight line.

Two natural effects that result from the rectilinear propagation of light are the formation of eclipses and shadows. The principle of operation of the pinhole camera also depends on the fact that light travels in straight lines.

What is a shadow?

A shadow is an area in which light rays from a source cannot reach. It is produced by the obstruction of light by an opaque object. There are two types of shadow: partial (penumbra) shadow and total (umbra) shadow.

If the light source is large, the shadow formed consists of two parts: a completely dark area known as the umbra and an outer grey area known as the penumbra or partial shadow.

In the umbra region, the light from the source is completely blocked by the opaque body. In the penumbra region, the light is partially blocked by the opaque object. The inner region of the shadow receives less light than the outer parts. Thus the penumbra becomes brighter from the umbra outwards.

What is an eclipse?

An eclipse is a result of a shadow cast by one heavenly body on another. The sun is a luminous body in the middle. The earth revolves around the sun and the moon revolves around the earth. If the moon is between the sun and the earth, the shadow of the moon will be cast on the earth’s surface.

There are two types of eclipse:

1. Eclipse of the sun (solar eclipse): here the moon comes between the sun and the earth in a straight line.
2. Eclipse of the moon (lunar eclipse): in this case, the earth comes in between the sun and the moon.

How does a pinhole camera work?

A pinhole camera consists of a lightproof box, one end of which has a small hole made with a pin or needlepoint. The opposite end has a screen made with tracing paper or ground glass. Light from an object in front of the pinhole passes through it and forms an image on the screen. If the screen is replaced with photographic paper or film, a picture of the object can be taken with the pinhole camera.

When using the pinhole camera to take pictures of an object, a long exposure is necessary to allow sufficient light to enter the box through the pinhole. The image formed on the screen will be seen more clearly if external light is excluded by covering the head and camera with a dark cloth.

The image formed on the screen of the pinhole camera is inverted.

Linear magnification

Magnification is defined as the ratio of the size (or height) of the image to the size (or height) of the object.

Image magnification = image size / object size = image distance / object distance

i.e. M = h_i / h_o = v / u

What is reflection of light waves?

Reflection is the bouncing back of light waves when they strike a surface.

Types of reflection

1. Regular reflection
2. Diffuse or irregular reflection

In regular reflection, parallel rays of light incident on a smooth or polished surface are reflected as parallel rays in one direction.

In diffuse or irregular reflection, parallel rays of light incident on a rough or irregular surface are reflected in various directions.

Laws of reflection

The first law of reflection states that the incident ray, the reflected ray and the normal at the point of incidence all lie on the same plane.

The second law of reflection states that the angle of incidence (i) is equal to the angle of reflection (r).

How does a plane mirror form an image?

Characteristics of the image formed by a plane mirror

1. It is the same size as the object.
2. It is virtual.
3. It is laterally inverted.
4. It is upright.
5. It is as far behind the mirror as the object is in front of the mirror.

Real and virtual images

There are two types of image: real and virtual.

A real image can be caught on a screen. Light rays pass through real images. A virtual image cannot be caught on a screen. It is one through which rays do not pass but which is nevertheless visible.

Lateral inversion

Lateral inversion is the effect of a plane mirror on objects placed in front of it, whereby the image looks like a reversal of the object.

Images formed by inclined mirrors

When two mirrors are placed at an angle to each other, the number of images formed is given by:

n = (360° / θ) – 1

where n = number of images and θ = angle of inclination.

When θ = 180°, the two mirrors act as a single mirror and therefore form only one image. When θ = 0°, the two mirrors are parallel to each other and the image of an object placed between them will be at infinity.

Effect of mirror rotation on the reflected ray: the mirror galvanometer

If the direction of an incident ray on a mirror is kept constant and the mirror is rotated through an angle, the reflected ray turns through twice that angle. This fact is used in mirror galvanometers (to measure very small electric currents) and in the navigator’s sextant.

Example

The reflection of a narrow beam of light incident normally on a plane mirror falls on a metre rule parallel to the mirror and at a distance of 1 m. Calculate the angle of rotation of the mirror if the reflected beam is displaced 21.26 cm along the metre rule when the mirror rotates.

Solution

Angle ONP = 2θ
tan 2θ = 21.26 / 100 = 0.2126
2θ = tan^-1 (0.2126)
2θ = 12°
θ = 6°

Uses of plane mirrors

1. It is used in the periscope.
2. It is used in the kaleidoscope.
3. It is used in the sextant.

How do curved mirrors reflect light?

Curved mirrors differ in size, shape and direction of their curvature. In respect of shape, we have spherical and parabolic mirrors.

There are two types of spherical mirror: concave and convex.

1. Concave mirrors are hollowed out toward the incident light, like the inside surface of a spoon. A concave mirror is also called a converging mirror.
2. Convex mirrors bulge towards the incident light, like the back of a spoon. A convex mirror is also called a divergent mirror.

Terms used with spherical mirrors

1. The pole (p): the midpoint of the spherical mirror.
2. The aperture: the width or diameter of the mirror.
3. The centre of curvature (c): the centre of the large sphere from which the spherical mirror is carved out.
4. The radius of curvature (R): the distance between the centre of curvature and the pole of the mirror.
5. The principal axis: the imaginary line passing through the pole (p) and the centre of curvature (c).
6. The principal focus (f): the point on the principal axis where the incident rays converge (for concave mirrors) or appear to diverge (for convex mirrors).
7. Focal length (f): the distance between the focus and the pole of the spherical mirror. It is always half of the radius of curvature.

f = R/2

R = 2f

Spherical aberration

Spherical aberration is the phenomenon whereby a spherical mirror of a wide aperture cannot bring all parallel rays to the same focus. To avoid this, spherical mirrors of a small aperture are usually used. This is also why parabolic mirrors are used in place of spherical mirrors in searchlights and car headlamps.

How do you construct ray diagrams for curved mirrors?

The following rules are used in constructing ray diagrams:

1. Light rays parallel to the principal axis are reflected through the focus.
2. A light ray passing through the centre of curvature is reflected along the same path.
3. A light ray passing through the focus is reflected parallel to the principal axis.
4. Light rays striking the mirror at the pole are reflected such that the angle of incidence is equal to the angle of reflection.

What images do concave and convex mirrors form?

Images formed by concave mirrors

Images formed by convex mirrors

The image formed by a convex mirror is always virtual, erect and diminished in size. It is formed between the pole and the principal focus. This is unlike the concave mirror, which can produce either real or virtual images that may be inverted or erect, magnified or diminished in size, according to the position of the object.

What are linear magnification and the mirror formula?

Linear magnification

Linear magnification is the ratio of the image size to the object size.

Image size / object size = image distance / object distance

i.e. M = h_i / h_o = v / u

Mirror formula

The focal length, f, the object distance, u, and the image distance, v, are related by the formula:

1/u + 1/v = 1/f

What is sign convention?

Sign convention is used to give the correct signs to all the quantities used in mirror calculations. Two conventions are in use:

1. The new Cartesian convention: all distances measured to the left of the mirror from the pole are negative, while distances measured to the right of the mirror from the pole are positive.
2. Real is positive and virtual is negative: this is the most widely accepted and used in calculations for mirrors and lenses. In this case:

• All distances are measured from the pole of the mirror to either left or right.
• The distance between real objects and real images is positive.
• The distance between virtual objects and virtual images is negative.
• The focal length of a concave mirror is positive, while the focal length of a convex mirror is negative.

Example

An object which is 5.0 cm high is placed 10.0 cm in front of a convex mirror of focal length 15.0 cm. Find the position, size and nature of the image produced.

Solution

Using “real is positive”: f = -15 cm, u = 10 cm

1/u + 1/v = 1/f
1/10 + 1/v = -1/15
1/v = -1/15 – 1/10 = -(5/30)
v = -6 cm

For magnification:
m = v/u
m = -(6/10)
m = -0.6

Image size = magnification × object size (height)
Image size = 0.6 × 5.0 = 3.0 cm

Thus, the image is formed 6.0 cm behind the mirror and its height is 3.0 cm. It is erect, virtual and diminished.

Evaluation

1. State the two laws of reflection.
2. Distinguish between regular reflection and diffuse reflection.
3. List four characteristics of the image formed by a plane mirror.
4. Two plane mirrors are inclined at 60° to each other. How many images of an object placed between them are formed?
5. State the relationship between the focal length and the radius of curvature of a spherical mirror.

Assignment

1. (a) Give the differences between a real and a virtual image.
   (b) A magnified, virtual image is formed 12 cm from a concave mirror of focal length 18 cm. Calculate the position of the object and the magnification of the image.
2. (a) Explain, with the aid of a diagram, how the image of an object is formed by a plane mirror.
   (b) State four characteristics of the image.
3. (a) Define the following terms: (i) principal focus (ii) radius of curvature.
   (b) The screen of a pinhole camera is a square of side 160 mm and it is 150 mm behind the pinhole. The camera is placed 11 m from a flagstaff and positioned so that the image of the flagstaff is formed centrally on the screen. The image occupies three-quarters of the screen. What is the length of the staff?