Chapter 11: Reflection of Light
Comprehensive chapter summary with detailed explanations and examples.
Grade 9 Learning: Chapter 11: Reflection of Light
Introduction to Light and Reflection
Light is a form of energy that enables us to see the world around us. It travels in straight lines. When light falls on a surface, it can be absorbed, transmitted, or reflected. **Reflection of light** is the phenomenon of light bouncing back after striking a surface.
What is Reflection?
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include light bouncing off a mirror or sound echoing off a wall.
Laws of Reflection
Reflection of light follows two fundamental laws:
1. First Law of Reflection
The incident ray, the reflected ray, and the normal to the surface at the point of incidence, all lie in the same plane.
Understanding the Terms:
- Incident Ray: The ray of light that falls on the surface.
- Reflected Ray: The ray of light that bounces back from the surface.
- Normal: An imaginary line perpendicular to the surface at the point where the incident ray strikes it.
- Point of Incidence: The point on the surface where the incident ray strikes.
2. Second Law of Reflection
The angle of incidence ($\angle i$) is equal to the angle of reflection ($\angle r$).
$\angle i = \angle r$
Angles Explained:
- Angle of Incidence ($\angle i$): The angle between the incident ray and the normal.
- Angle of Reflection ($\angle r$): The angle between the reflected ray and the normal.
This law implies that if a light ray strikes a mirror at an angle of 30 degrees to the normal, it will reflect at an angle of 30 degrees to the normal.
Types of Reflection
The nature of the reflected light depends on the type of surface it strikes.
1. Regular (Specular) Reflection
- Occurs when light strikes a smooth, polished surface (like a mirror).
- Parallel incident rays reflect as parallel reflected rays.
- Forms clear and sharp images.
- Example: Reflection from a plane mirror, still water surface.
2. Diffused (Irregular) Reflection
- Occurs when light strikes a rough or uneven surface.
- Parallel incident rays reflect in various directions.
- Does not form clear images, but allows us to see objects from different angles.
- Example: Reflection from a wall, paper, clothes.
Mirrors
Mirrors are polished surfaces that reflect almost all the light falling on them. They are broadly classified into plane mirrors and spherical mirrors.
1. Plane Mirror
A plane mirror is a flat, smooth, polished surface that reflects light regularly.
Image Formation by a Plane Mirror
- Virtual: The image appears to be formed behind the mirror and cannot be obtained on a screen.
- Erect: The image is upright, the same orientation as the object.
- Same size as the object: The height of the image is equal to the height of the object.
- Laterally inverted: The left side of the object appears as the right side of the image, and vice-versa.
- Located as far behind the mirror as the object is in front of it: The object distance equals the image distance.
Real-world example:
When you look at yourself in a bathroom mirror, you see an erect, virtual image that is the same size as you, but your left hand appears as your right hand in the reflection (lateral inversion).
2. Spherical Mirrors
Spherical mirrors are part of a hollow sphere whose one surface is polished to reflect light. They can be concave or convex.
Key Terms for Spherical Mirrors:
- Pole (P): The geometric center of the mirror's reflecting surface.
- Centre of Curvature (C): The center of the sphere of which the mirror is a part.
- Radius of Curvature (R): The distance between the pole and the centre of curvature (R = PC).
- Principal Axis: The straight line passing through the pole and the centre of curvature.
- Principal Focus (F): The point on the principal axis where rays parallel to the principal axis converge after reflection (concave mirror) or appear to diverge from after reflection (convex mirror).
- Focal Length (f): The distance between the pole and the principal focus (f = PF). For spherical mirrors, $f = R/2$.
- Aperture: The effective diameter of the spherical mirror.
a. Concave Mirror (Converging Mirror)
A spherical mirror whose inner (concave) surface is the reflecting surface.
Image Formation by Concave Mirror (Ray Diagrams):
- Rule 1: A ray parallel to the principal axis, after reflection, passes through the principal focus (F).
- Rule 2: A ray passing through the principal focus (F), after reflection, becomes parallel to the principal axis.
- Rule 3: A ray passing through the centre of curvature (C), after reflection, retraces its path.
- Rule 4: A ray incident at the pole (P) is reflected obliquely, making the same angle with the principal axis.
Nature of Images formed by Concave Mirror (Summary Table):
| Position of Object | Position of Image | Nature of Image | Size of Image |
|---|---|---|---|
| At infinity | At F | Real, Inverted | Highly diminished (point size) |
| Beyond C | Between F and C | Real, Inverted | Diminished |
| At C | At C | Real, Inverted | Same size |
| Between C and F | Beyond C | Real, Inverted | Enlarged |
| At F | At infinity | Real, Inverted | Highly enlarged |
| Between F and P | Behind the mirror | Virtual, Erect | Enlarged |
Uses of Concave Mirrors:
- Shaving mirrors / Dentist mirrors: To see enlarged images of face/teeth.
- Headlights of cars / Torches: To get a powerful parallel beam of light (object at F).
- Solar furnaces: To concentrate sunlight at the focus.
- Reflecting telescopes: As primary mirrors.
b. Convex Mirror (Diverging Mirror)
A spherical mirror whose outer (convex) surface is the reflecting surface.
Image Formation by Convex Mirror (Ray Diagrams):
- Rule 1: A ray parallel to the principal axis, after reflection, appears to diverge from the principal focus (F).
- Rule 2: A ray directed towards the principal focus (F), after reflection, becomes parallel to the principal axis.
- Rule 3: A ray directed towards the centre of curvature (C), after reflection, retraces its path.
- Rule 4: A ray incident at the pole (P) is reflected obliquely, making the same angle with the principal axis.
Nature of Images formed by Convex Mirror (Summary Table):
| Position of Object | Position of Image | Nature of Image | Size of Image |
|---|---|---|---|
| At infinity | At F (behind mirror) | Virtual, Erect | Highly diminished (point size) |
| Anywhere between infinity and P | Between P and F (behind mirror) | Virtual, Erect | Diminished |
Uses of Convex Mirrors:
- Rear-view mirrors in vehicles: Provide a wider field of view and always form erect, diminished images.
- Shop security mirrors: To monitor a large area.
- Street light reflectors: To spread light over a larger area.
Sign Convention for Reflection by Spherical Mirrors (New Cartesian Sign Convention)
To accurately describe image formation and perform calculations, a standard sign convention is used:
- The pole (P) of the mirror is taken as the origin (0,0).
- The principal axis is taken as the X-axis.
- Distances measured to the right of the origin along the principal axis are taken as positive.
- Distances measured to the left of the origin along the principal axis are taken as negative.
- Distances measured perpendicular to and above the principal axis are taken as positive.
- Distances measured perpendicular to and below the principal axis are taken as negative.
- The focal length of a concave mirror is negative, and that of a convex mirror is positive.
Mirror Formula and Magnification
These formulas relate object distance ($u$), image distance ($v$), and focal length ($f$) for spherical mirrors.
Mirror Formula:
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
- $u$: Object distance (distance of the object from the pole).
- $v$: Image distance (distance of the image from the pole).
- $f$: Focal length of the mirror.
Magnification ($M$):
Magnification describes the relative size of the image with respect to the object. It is defined as the ratio of the height of the image to the height of the object.
$M = \frac{h'}{h} = -\frac{v}{u}$
- $h'$: Height of the image.
- $h$: Height of the object.
- If $M$ is positive, the image is erect and virtual.
- If $M$ is negative, the image is inverted and real.
- If $|M| > 1$, the image is enlarged.
- If $|M| < 1$, the image is diminished.
- If $|M| = 1$, the image is of the same size.
Conclusion
Reflection of light is a fundamental concept in optics, governed by two simple laws. Mirrors, both plane and spherical, exhibit this phenomenon to form images with distinct characteristics. Understanding ray diagrams, sign conventions, and mirror formulas is crucial for analyzing how light interacts with mirrors and for various practical applications in daily life and technology.
References
- Maharashtra State Board Science and Technology Standard Nine Textbook (Latest Edition) - Chapter 11: Reflection of Light.
- Maharashtra State Board 9th Standard Science Syllabus.
- Balbharati Science and Technology Textbook Part 1.
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