Chapter 9: LIGHT – REFLECTION AND REFRACTION
Introduction
Light is a form of energy that enables us to see things. It travels in a straight line in a medium and shows several important phenomena such as reflection, refraction, dispersion, and total internal reflection.
1. Reflection of Light
Reflection is the phenomenon in which light rays strike a smooth surface and bounce back into the same medium.
Laws of Reflection:
- The angle of incidence (i) is equal to the angle of reflection (r).
- The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
2. Types of Reflection
- Regular Reflection: When light reflects from a smooth surface like a mirror, parallel rays remain parallel. It forms a clear image.
- Irregular Reflection (Diffuse Reflection): When light reflects from a rough surface, the rays scatter in different directions, and no image is formed.
3. Spherical Mirrors
Mirrors whose reflecting surfaces are part of a sphere are called spherical mirrors. They are of two types:
- Concave Mirror: Reflecting surface is inward, curved like the inside of a spoon.
- Convex Mirror: Reflecting surface is outward, curved like the back of a spoon.
4. Important Terms Related to Spherical Mirrors
- Pole (P): The center of the mirror’s reflecting surface.
- Center of Curvature (C): The center of the sphere from which the mirror is made.
- Radius of Curvature (R): Distance between C and P.
- Principal Axis: The line joining C and P.
- Focus (F): The point where light rays parallel to the principal axis meet (concave) or appear to diverge from (convex).
- Focal Length (f): Distance between P and F.
Relation: f = R / 2
5. Mirror Formula
The relationship between object distance (u), image distance (v), and focal length (f) is:
1/f = 1/v + 1/u
Sign Convention (New Cartesian Sign Convention):
- All distances are measured from the pole (P).
- Distances measured in the direction of the incident light are positive.
- Distances measured opposite to the direction of the incident light are negative.
- Heights above the principal axis are positive; below are negative.
6. Image Formation by Concave Mirror
Cases:
- Object beyond C → Image between F and C → Real, inverted, smaller.
- Object at C → Image at C → Real, inverted, same size.
- Object between C and F → Image beyond C → Real, inverted, larger.
- Object at F → Image at infinity → Real, inverted, very large.
- Object between F and P → Image behind the mirror → Virtual, erect, enlarged.
Uses of Concave Mirror:
- Used in shaving mirrors and makeup mirrors.
- Used in reflecting telescopes.
- Used by dentists to view enlarged images of teeth.
7. Image Formation by Convex Mirror
- Always forms a virtual, erect, and diminished
- Image appears behind the mirror between the pole (P) and focus (F).
Uses:
- Used as a rear-view mirror in vehicles because it gives a wider field of view.
8. Magnification by Mirrors
Magnification (m) = Height of image (h’) / Height of object (h)
Also,
m = –v / u
If m is positive → image is virtual and erect.
If m is negative → image is real and inverted.
9. Refraction of Light
Refraction is the phenomenon of bending of light when it passes from one medium to another due to a change in its speed.
Example:
A pencil partly dipped in water appears bent due to refraction.
10. Laws of Refraction
- The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
- The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for the same pair of media.
This constant is called the Refractive Index (n):
n = sin i / sin r
11. Refractive Index
- The refractive index represents how much a medium can bend light.
- If light travels from air to glass: n = speed of light in air / speed of light in glass
- The greater the refractive index, the slower the speed of light in that medium.
Example:
Refractive index of water = 1.33
Refractive index of glass = 1.5
12. Refraction through a Rectangular Glass Slab
When light passes through a rectangular glass slab:
- It bends towards the normal while entering the denser medium (glass).
- It bends away from the normal while emerging into the rarer medium (air).
- The emergent ray is parallel to the incident ray but displaced sideways.
This shift is called Lateral Displacement.
13. Spherical Lenses
A transparent medium bounded by two curved surfaces or one curved and one plane surface is called a lens.
Types of Lenses:
- Convex Lens (Converging Lens): Thicker in the middle, thinner at edges.
- Concave Lens (Diverging Lens): Thinner in the middle, thicker at edges.
14. Important Terms Related to Lenses
- Optical Center (O): The center of the lens through which light passes undeviated.
- Principal Axis: The line joining the centers of curvature of both spherical surfaces.
- Principal Focus (F): The point where light rays parallel to the principal axis converge (convex) or appear to diverge (concave).
Focal Length (f): Distance between optical center and focus.
15. Lens Formula
1/f = 1/v – 1/u
(where u is the object distance, v is image distance, and f is focal length)
Magnification (m):
m = h’/h = v/u
16. Image Formation by Convex Lens
- Object beyond 2F → Image between F and 2F → Real, inverted, smaller.
- Object at 2F → Image at 2F → Real, inverted, same size.
- Object between F and 2F → Image beyond 2F → Real, inverted, larger.
- Object at F → Image at infinity → Real, inverted, highly enlarged.
- Object between F and O → Image on same side → Virtual, erect, enlarged.
Uses:
Used in magnifying glass and cameras
17. Image Formation by Concave Lens
Always forms a virtual, erect, and diminished image on the same side of the lens as the object.
Uses:
- Used in spectacles for people with myopia (near-sightedness).
18. Power of a Lens
Power of a lens measures its ability to converge or diverge light rays.
Power (P) = 1 / focal length (in meters)
Unit: Dioptre (D)
1 D = 1 m⁻¹
If f is in meters:
- For convex lens (converging): P is positive
- For concave lens (diverging): P is negative
19. Combination of Lenses
When two or more lenses are placed in contact, the total power is the sum of their individual powers.
P = P₁ + P₂ + P₃ …
20. Applications of Lenses and Mirrors
- Concave mirror → used in shaving mirrors, headlights.
- Convex mirror → used in rear-view mirrors.
- Convex lens → used in magnifying glasses, cameras.
- Concave lens → used in spectacles.
21. Common Ray Diagrams in Lenses and Mirrors
- Ray parallel to the principal axis passes through the focus (for concave mirror/convex lens).
- Ray passing through the center of curvature retraces its path (for mirrors).
- Ray passing through optical center passes undeviated (for lenses).
22. Sign Conventions for Lenses
- All distances are measured from the optical center (O).
- Distances measured in the direction of incident light are positive.
- Opposite direction distances are negative.
- Heights above the principal axis are positive; below are negative.
23. Numerical Relations
- Mirror Formula: 1/f = 1/v + 1/u
- Lens Formula: 1/f = 1/v – 1/u
- Magnification: m = h’/h = v/u
- Power: P = 1/f (f in meters)
24. Real and Virtual Images – Summary
Mirror/Lens | Nature of Image | Type | Orientation |
Concave Mirror | Real or Virtual | Inverted or Erect | Larger/Smaller |
Convex Mirror | Always Virtual | Erect | Diminished |
Convex Lens | Real or Virtual | Inverted or Erect | Varies |
Concave Lens | Always Virtual | Erect | Diminished |
25. Practical Uses in Daily Life
- Concave mirrors in torches, solar furnaces.
- Convex mirrors for safety and vehicle mirrors.
- Convex lenses in microscopes, projectors.
- Concave lenses for correcting myopia.
Conclusion
The study of light’s reflection and refraction helps us understand how images form in mirrors and lenses. These concepts are used in various optical instruments such as cameras, microscopes, and human eyes.