1. The Nature of Light
Visibility of Objects
Objects become visible because they reflect light falling on them.
When this reflected light enters our eyes, we perceive the object.
Propagation of Light
Light generally travels in straight lines. This can be observed
when small light sources produce sharp shadows of opaque objects.
Theories of Light
-
Ray Optics: Treats light as travelling along straight-line paths
called rays.
-
Wave Theory: Required to explain phenomena such as diffraction,
where light bends around very small obstacles.
-
Particle Theory: Explains the interaction of light with matter
as a stream of particles.
-
Modern Quantum Theory: Light exhibits both wave-like and
particle-like characteristics.
Important Concept
Light cannot be described completely as only a wave or only a particle.
It exhibits
wave-particle duality.
2. Reflection of Light
Reflection from Mirrors
Highly polished surfaces, such as mirrors, reflect most of the
incident light falling on them.
Laws of Reflection
First Law: The angle of incidence is equal to the angle
of reflection.
∠i = ∠r
Second Law: The incident ray, the normal at the point
of incidence, and the reflected ray all lie in the same plane.
Image Formed by a Plane Mirror
- The image is always virtual and erect.
- The image is of the same size as the object.
-
The image distance behind the mirror equals the object
distance in front of the mirror.
- The image is laterally inverted.
Lateral Inversion
The left side of an object appears as the right side in its
mirror image, and vice versa.
3. Spherical Mirrors: Core Concepts
Types of Spherical Mirrors
Concave Mirror
A spherical mirror whose reflecting surface is curved
inwards, facing the centre of the sphere.
Convex Mirror
A spherical mirror whose reflecting surface is curved
outwards.
Important Terminology
| Term |
Meaning |
| Pole (P) |
The centre of the reflecting surface of the mirror.
|
| Centre of Curvature (C) |
The centre of the sphere of which the mirror is a part.
It is not located on the mirror surface.
|
| Radius of Curvature (R) |
The distance between the pole and the centre of curvature.
|
| Principal Axis |
The straight line passing through P and C.
|
| Principal Focus (F) |
The point where parallel rays converge, or from which
they appear to diverge.
|
| Focal Length (f) |
The distance between the pole and the principal focus.
|
| Aperture |
The diameter of the circular outline of the reflecting surface.
|
R = 2f
For spherical mirrors of small aperture, the radius of curvature
is approximately twice the focal length.
4. Image Formation by Spherical Mirrors
Concave Mirror
| Object Position |
Image Position |
Size |
Nature |
| At infinity |
At focus F |
Highly diminished |
Real and inverted |
| Beyond C |
Between F and C |
Diminished |
Real and inverted |
| At C |
At C |
Same size |
Real and inverted |
| Between C and F |
Beyond C |
Enlarged |
Real and inverted |
| At F |
At infinity |
Highly enlarged |
Real and inverted |
| Between P and F |
Behind the mirror |
Enlarged |
Virtual and erect |
Convex Mirror
| Object Position |
Image Position |
Size |
Nature |
| At infinity |
At F behind the mirror |
Highly diminished |
Virtual and erect |
| Between infinity and P |
Between P and F behind the mirror |
Diminished |
Virtual and erect |
Remember
A convex mirror always forms a
virtual, erect and diminished
image, regardless of the object's position.
5. Practical Applications of Mirrors
Concave Mirrors
-
Torches and searchlights: Produce powerful parallel beams
when the source is placed at the focus.
-
Vehicle headlights: Used to obtain parallel beams of light.
-
Shaving mirrors: Produce enlarged images of the face
when the face is placed within the focal length.
-
Dentists: Used to obtain enlarged images of teeth.
-
Solar furnaces: Concentrate sunlight at a point to produce
high temperatures.
Convex Mirrors
Convex mirrors are used as rear-view or wing mirrors in vehicles.
They provide an erect image and a
wider field of view because of their outward curvature.
6. Reflection Formula and Sign Convention
New Cartesian Sign Convention
-
The object is placed on the left side of the mirror.
-
All distances are measured from the pole of the mirror.
-
Distances measured to the right are positive.
-
Distances measured to the left are negative.
-
Heights above the principal axis are positive.
-
Heights below the principal axis are negative.
Mirror Formula
1/v + 1/u = 1/f
Where:
- u = object distance
- v = image distance
- f = focal length
Magnification
m = h' / h = −v / u
- m = magnification
- h' = height of image
- h = height of object
Sign of Magnification
Negative magnification generally indicates a
real and inverted image.
Positive magnification indicates a
virtual and erect image.
7. Refraction of Light
Definition
Refraction is the change in direction of light when it travels
obliquely from one transparent medium to another due to a change
in its speed.
Laws of Refraction
-
The incident ray, 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 a given pair of media.
Snell's Law
sin i / sin r = constant
Refractive Index
The refractive index describes how much light slows down when
entering a medium.
n₂₁ = Speed of light in medium 1 / Speed of light in medium 2
Absolute Refractive Index
n = c / v
- c = speed of light in vacuum
-
c ≈ 3 × 108 m/s
- v = speed of light in the medium
Optical Density and Bending of Light
Rarer → Denser
Light slows down and bends
towards the normal.
Denser → Rarer
Light speeds up and bends
away from the normal.
8. Refraction by Spherical Lenses
Types of Lenses
Convex Lens
A converging lens that is thicker at the middle
and thinner at the edges.
It converges parallel rays to a principal focus.
Concave Lens
A diverging lens that is thinner at the middle
and thicker at the edges.
It causes parallel rays to diverge as if they
originate from a focus.
Lens Formula
1/v − 1/u = 1/f
Magnification
m = h' / h = v / u
Power of a Lens
The power of a lens is the reciprocal of its focal length
measured in metres.
P = 1/f
- SI unit = Dioptre (D)
- 1 D = 1 m−1
- Convex lens has positive power.
- Concave lens has negative power.
Combination of Lenses
When lenses are placed in contact, their powers add up.
P = P₁ + P₂ + P₃ + ...
Important Reminder
Focal length must be expressed in
metres when calculating
the power of a lens in dioptres.