Light rays

• Light waves
• Source of Light waves
• Reflection of Light waves
• Reflection of plane and curved mirrors

Light waves

Light wave is a visible source of energy. It is also a wave motion. It has a very short wavelength of 5×10^-4mm. Light travels at a speed of 3.0×10⁸ms^-1

Source of Light waves

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 the candle, electric torch, the electric lamp, incandescent, arc light and fluorescent light.

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

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

When light falls on such surface, it is may be absorbed, transmitted or reflected, sometimes a combination of the above processes may occur

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

RECTILINEAR PROPAGATION OF LIGHT

The phenomenon of light travelling in 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, light of the flame will be seen clearly at the other side of the pipe. If the pipe is then bent and the process repeated, nothing will be seen at the other end, this clearly shows that light travels in straight line. Two natural effects that result from the rectilinear propagation of light are the formation of eclipse and shadow, The principle of operation of the pin hole camera also depends on the fact that light travels in straight lines.

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 consist of two parts, a completely dark area known as umbra and an outer grey area known as 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 than the outer parts. Thus the penumbra becomes brighter from the umbra and outwards.

ECLIPSE

An eclipse is a result of a shadow cast by one heavenly body on another. The sun being a luminous body and it is in the middle while the earth and the moon revolves round the sun. 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 the eclipse. Viz:

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.

PIN HOLE CAMERA

It consists of a light proof box, one end of which has a small hole made with a pin or needle point. 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 form an image on the screen. If the screen is replaced with a 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, long exposure is necessary to allow sufficient light to enter the box through the pin hole. The image formed on the screen of the pinhole camera will be seen more clearly if external light is excluded by covering head and camera with a dark cloth.

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

Reflection of Light waves

Reflection is the bouncing back of light waves when it strikes a surface.

Reflection of plane mirrors

There are two types of reflection:

1.       Regular Reflection

2.       Diffuse Reflection 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.

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 angle of reflection (r).

IMAGE FORMATION BY A PLANE MIRROR

CHARACTERISTICS OF IMAGE FORMED BY 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 far behind the mirror as the object is in front of the mirror

IMAGE

There are two types of image:

1.       Real image

2.       Virtual image

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

LATERAL INVERSION

The effect on plane mirror on objects placed in front of it whereby the appearance of the image looks like a reversal of the object is known as lateral inversion

EFFECT OF MIRROR ROTATION ON REFLECTED RAY-MIRROR GALVANOMETER

If the direction of an incident ray on a mirror is kept constant and the mirror is rotated through twice that angle.  This fact is utilized in mirror galvanometer (to measure very small electric current) and in the navigator’s sextant.

USES OF PLANE MIRROR

It is used in periscope

It is used in kaleidoscope It is used in sextant

Reflection of curved mirrors

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 mirrors – concave and convex mirrors

1. Concave mirrors – the concave mirrors are hollowed-out toward the incident light like the inside surface of a spoon. It is also called a converging mirror.
2. Convex mirrors – these mirrors bulge towards the incident light like he back of a spoon. Convergent mirrors are also referred to as divergent mirrors.

Terms used with spherical mirrors

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

Spherical aberration

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

Construction of ray diagrams

The following tips are used in constructing ray diagrams

1. Light rays parallel to principal axis are reflected through the focus
2. A light ray passing through the center of the curvature is reflected back 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 is reflected such that the angle of incidence is equal to the angle of reflection

Characteristics of image formed by concave mirrors

1. Object before center of curvature: the image formed is:
2. same size the object
3. between the center of curvature and the focus
4. inverted
5. real
6. Object at the center of curvature: the image formed is
7. same size the object
8. at the center of curvature
9. inverted
10. real
11. Object between the center of curvature and the focus: the image formed is
12. Magnified
13. Beyond the center of curvature
14. Inverted
15. real
16. Object at focus: the image formed is
17. Formed at infinity
18. Object between focus and the pole: the image formed is
19. Magnified
20. Behind the mirror
21. Virtual
22. Erect
23. Object at infinity: the image formed is
24. Diminished
25. Formed at the focus
26. Real
27. Inverted

Characteristics of image 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 case of 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.

Sign convention

This is used to know and calculate by properly assigning sign to all the parameters used in mirror

1. The new Cartesian – here, all the distances measure 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:
3. All distances are measured from the pole of the mirror to either left or right
4. The distance of real objects and real images are positive
5. The distance of virtual objects and virtual images are negative
6. The focal length of a concave mirror is positive while the focal length of a convex mirror is negative

Concave Mirrors and Convex Mirrors Ray Diagram – Equations / Formulas & Practice Problems

CLASSWORK 10

1. (a) What do you understand by the term lateral inversion? (b) write your first name in block form to buttress (a)
2. Differentiate between concave and convex mirror
3. Two plane mirrors inclining at an unknown angle, forms 11 images. Find the value of the angle
4. Mention three uses of plane mirrors

ASSIGNMENT 10

SECTION A

1. Which of the following abatement is true of virtual image (a) it is formed on the screen (b) it is formed by the intersection of actual rays (c) rays of light do not pass through it (d) all of the above (e) none of the above
2. An object is placed between two plane mirrors inclined at 60⁰ to each other. How many images will the observer see? (a) 6 (b) 5 (c) 4 (d) 3 (e) 2
3. An object is place 15cm in front of a concave mirror of focal length 20cm, the image formed is (a) real, inverted and diminished (b) real, inverted and magnified (c) virtual, erect and diminished (d) virtual, erect and magnified (e) virtual, inverted and magnified
4. A concave mirror can be used to produce can be used to produce a parallel beam of light if a light bulb is placed (a) between its focus and the pole (b) at its focus (c) at its center of curvature (d) between its focus and the center of curvature (e) none of the above
5. When an image is formed in a plane mirror, the image formed will be (a) the same size as the object (b) smaller than the object  (c) laterally inverted (d) always virtual (e) all of the above
6. Using the real is positive sign convention determine the sign of the focal length of a convex mirror (a) positive (b) negative (c) neutral (d) none of the above (e) options (a) and (b)
7. An object is placed in front of a concave mirror of radius of curvature 12cm. if the height of the real image formed is three times that of the object, calculate the distance of the object from the mirror (a) 24 cm (b) 16 cm (c) 12 cm (d) 8 cm (e) 4 cm
8. A magnified erect image four times the size of the object is formed by a concave mirror of focal length 12cm. what is the distance of the image from the pole of the mirror? (a) -36cm (b) -18cm (c) -24cm (d) -3.6cm (e) 24cm
9. A boy walks away from a plane mirror at a constant speed of 5.0ms^-1 in a direction normal to the surface of the mirror. At what speed does his image move away from him? (a) 5.0ms^-1 (b) 2.50ms^-1 (c) 3.5.0ms^-1 (d) 1.25.0ms^-1 (e) 0.00ms^-1
10. The image of an object is located 6cm behind a convex mirror. if its magnification is 0.6, calculate the focal length of the mirror (a) 3.75 cm (b) 6.60 cm (c) 10.00 cm (d) 15.00 cm (e) 20.00 cm

SECTION B

• (a) Give the differences between real and a virtual image

(b) A magnified, virtual image is formed 12cm from a concave mirror of focal length 18cm. calculate the position of the object and the magnification of the image

• (a) Explain with the aid of diagram how the image of an object is formed by a plane mirror

(b) State four characteristics of the image

•  (a) Define the following terms (i) principal focus (ii) radius of curvature (iii) principal focus

(b) The screen of a pinhole camera is a square of side 160mm and it is 150mm behind the pole. The camera is placed 11m from a flag staff and positioned so that the image of the flag staff is formed centrally on the screen. The image occupies three-quarters of the screen. What is the length of the staff?