Light
1. Introduction to Light
Light: A form of energy that enables us to see objects around us.
Key Properties:
Light itself is invisible, but its presence makes other objects visible.
Speed of Light: \(3 \times 10^8 \text{ m/s}\) in vacuum or air.
Light travels in straight paths (rectilinear propagation).
Light can travel through a vacuum.
2. Reflection of Light
Definition: The phenomenon of bouncing back of light rays when they strike the surface of an object.
Key Components:
Incident Ray: The incoming ray of light that strikes the surface.
Reflected Ray: The ray of light that bounces back from the surface.
Normal: An imaginary line drawn perpendicular to the surface at the point of incidence.
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.
Laws of Reflection:
First Law: The angle of incidence is equal to the angle of reflection (\(\angle i = \angle r\)).
Second Law: The incident ray, reflected ray, and normal at the point of incidence all lie in the same plane.
3. Image Formation by Plane Mirrors
Lateral Inversion: A phenomenon where the left side of an object appears as the right side in its mirror image, and vice versa.
Application: The word "AMBULANCE" is written laterally inverted on the front of ambulance vehicles so drivers ahead can read it correctly in their rear-view mirrors.
Characteristics of Images Formed by Plane Mirrors:
Virtual and Erect: Cannot be captured on a screen and is upright.
Same Size: The size of the image is equal to the size of the object.
Same Distance: The image is formed behind the mirror at the same distance as the object is in front of it.
Laterally Inverted.
Focal Length: The focal length of a plane mirror is infinite (\(\infty\)).
4. Spherical Mirrors
Spherical mirrors are curved mirrors whose reflecting surfaces form part of a hollow sphere.
Types of Spherical Mirrors:
Concave Mirror: Curved inwards (like a cave) with the outer side polished; acts as a converging mirror.
Convex Mirror: Curved outwards with the inner side polished; acts as a diverging mirror.
Key Terminology:
Pole (\(P\)): The midpoint or center of the reflecting surface.
Center of Curvature (\(C\)): The center of the sphere of which the mirror forms a part.
Radius of Curvature (\(R\)): The distance between the Pole (\(P\)) and Center of Curvature (\(C\)).
Principal Axis: The straight line passing through the Pole (\(P\)) and Center of Curvature (\(C\)).
Principal Focus (\(F\)): The midpoint between \(C\) and \(P\) where parallel light rays converge or appear to diverge.
Focal Length (\(f\)): The distance between the Focus (\(F\)) and Pole (\(P\)). \[\mathbf{R = 2f} \quad \text{or} \quad \mathbf{f = \frac{R}{2}} \quad\]
Aperture: The effective diameter of the circular reflecting surface.
Rules for Ray Diagrams (Spherical Mirrors):
A ray parallel to the principal axis passes through (or appears to diverge from) the principal focus after reflection.
A ray passing through (or directed towards) the focus becomes parallel to the principal axis after reflection.
A ray passing through the Center of Curvature (\(C\)) retraces its path back along the same path after reflection.
A ray incident obliquely at the pole reflects obliquely at the same angle with the principal axis.
5. Image Formation & Uses of Spherical Mirrors
Image Formation by Concave Mirror:
Object at Infinity: Image formed at \(F\); highly diminished (point-sized); Real & Inverted.
Object Beyond \(C\): Image formed between \(C\) and \(F\); diminished; Real & Inverted.
Object at \(C\): Image formed at \(C\); same size as object; Real & Inverted.
Object Between \(C\) and \(F\): Image formed beyond \(C\); enlarged; Real & Inverted.
Object at \(F\): Rays reflect parallel towards infinity; image is not formed / highly enlarged.
Object Between \(P\) and \(F\): Image formed behind the mirror; enlarged; Virtual & Erect.
Uses of Concave Mirrors:
Shaving & Makeup Mirrors: Provide a magnified upright view when the face is close.
Dentist Mirrors: Provide an enlarged view of teeth.
Solar Furnaces: Concentrate parallel sunlight at the focus to generate intense heat.
Headlights & Torches: Bulbs placed near the focus produce powerful parallel beams of light.
Image Formation by Convex Mirror:
Object at Infinity: Image formed at \(F\) (behind mirror); highly diminished (point-sized); Virtual & Erect.
Object at Any Finite Distance: Image formed between \(P\) and \(F\) (behind mirror); diminished; Virtual & Erect.
Uses of Convex Mirrors:
Rear-View Mirrors in Vehicles: Offer a wider field of view and form upright, diminished images of traffic behind.
Surveillance / Security Cameras: Used in shops and doorways for wider area visibility.
6. Sign Convention & Mirror Formula
New Cartesian Sign Convention:
Distances measured to the left of the pole (against incident light) are negative.
Distances measured to the right of the pole (along incident light) are positive.
Heights measured above the principal axis are positive.
Heights measured below the principal axis are negative.
Object Distance (\(u\)) is always negative.
Focal Length (\(f\)):
Concave Mirror: Negative.
Convex Mirror: Positive.
Mirror Formula: \[\mathbf{\frac{1}{v} + \frac{1}{u} = \frac{1}{f}} \quad\] (where \(v\) = image distance, \(u\) = object distance, \(f\) = focal length).
Magnification (\(m\)): \[\mathbf{m = \frac{\text{Height of Image }(h_i)}{\text{Height of Object }(h_o)} = -\frac{v}{u}} \quad\]
Negative \(m\): Image is Real and Inverted.
Positive \(m\): Image is Virtual and Erect.
\(|m| > 1\): Image is enlarged.
\(|m| < 1\): Image is diminished.
7. Refraction of Light
Definition: The phenomenon of bending of light rays when passing obliquely from one transparent medium to another due to a change in the speed of light.
Bending Behavior:
Rarer to Denser Medium: Light bends towards the normal.
Denser to Rarer Medium: Light bends away from the normal.
Laws of Refraction:
First Law: Incident ray, refracted ray, and normal at the point of incidence all lie in the same plane.
Second Law (Snell's Law): The ratio of the sine of the angle of incidence (\(\sin i\)) to the sine of the angle of refraction (\(\sin r\)) is constant for a given pair of media: \[\mathbf{\frac{\sin i}{\sin r} = \text{Constant}} \quad\]
Refraction through a Rectangular Glass Slab:
Light undergoes refraction twice (air-to-glass and glass-to-air).
Angle of incidence (\(\angle i\)) = Angle of emergence (\(\angle e\)).
The emergent ray is parallel to the incident ray but displaced laterally (Lateral Displacement).
8. Refractive Index (\(n\))
Definition: A measure of a medium's ability to bend light rays passing through it.
Key Relationships:
Higher Refractive Index \(\rightarrow\) Greater light bending ability.
Higher Refractive Index \(\rightarrow\) Greater optical density.
Higher Refractive Index \(\rightarrow\) Lower speed of light in that medium (\(n \propto \frac{1}{v}\)).
Absolute Refractive Index: \[\mathbf{n = \frac{c}{v}} \quad\] (where \(c = 3 \times 10^8 \text{ m/s}\) in vacuum/air, \(v\) = speed of light in medium). Refractive index of air is 1.
Relative Refractive Index:
Refractive index of Medium 2 with respect to Medium 1 (\(n_{21}\)): \[\mathbf{n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}} \quad\]
9. Refraction by Spherical Lenses
Spherical lenses are transparent optical materials bounded by two spherical surfaces.
Types of Lenses:
Convex Lens: Thicker at the center, thinner at the edges; acts as a converging lens.
Concave Lens: Thinner at the center, thicker at the edges; acts as a diverging lens.
Key Terminology:
Optical Center (\(O\)): Center point of the lens.
Principal Focus: Represented as \(F_1\) and \(F_2\) on either side of the lens.
Center points are represented as \(2F_1\) and \(2F_2\) instead of \(C\).
Rules for Ray Diagrams (Lenses):
A ray parallel to the principal axis passes through \(F_2\) (convex) or appears to diverge from \(F_1\) (concave).
A ray passing through \(F_1\) emerges parallel to the principal axis.
A ray passing through the Optical Center (\(O\)) passes straight without any bending (zero deviation).
Image Formation by Convex Lens:
Object at Infinity: Image formed at \(F_2\); point-sized; Real & Inverted.
Object Beyond \(2F_1\): Image formed between \(F_2\) and \(2F_2\); diminished; Real & Inverted.
Object at \(2F_1\): Image formed at \(2F_2\); same size as object; Real & Inverted.
Object Between \(2F_1\) and \(F_1\): Image formed beyond \(2F_2\); enlarged; Real & Inverted.
Object at \(F_1\): Image formed at infinity.
Object Between \(F_1\) and \(O\): Image formed on the same side as object; enlarged; Virtual & Erect.
Uses: Magnifying glasses, microscopes, telescopes, hypermetropia correction.
Image Formation by Concave Lens:
Object at Infinity: Image formed at \(F_1\); point-sized; Virtual & Erect.
Object at Any Finite Distance: Image formed between \(F_1\) and \(O\); diminished; Virtual & Erect.
Uses: Correction of myopia, door peepholes, laser flashlights, and torches.
10. Lens Formula, Magnification & Power of Lens
Lens Formula: \[\mathbf{\frac{1}{v} - \frac{1}{u} = \frac{1}{f}} \quad\]
Magnification for Lens (\(m\)): \[\mathbf{m = \frac{h_i}{h_o} = \frac{v}{u}} \quad\]
Sign Convention for Focal Length (\(f\)):
Concave Lens: Negative.
Convex Lens: Positive.
Power of a Lens (\(P\)):
Definition: The degree of convergence or divergence of light rays achieved by a lens.
Formulae: \[\mathbf{P = \frac{1}{f \text{ (in meters)}}} \quad \text{or} \quad \mathbf{P = \frac{100}{f \text{ (in cm)}}} \quad\]
SI Unit: Dioptre (\(D\)).
1 Dioptre Definition: The power of a lens whose focal length is \(1 \text{ meter}\) (\(1\text{ D} = 1\text{ m}^{-1}\)).
Power Signs:
Convex Lens: Positive Power.
Concave Lens: Negative Power.
Combination of Lenses: Net Power \(P_{\text{net}} = P_1 + P_2 + P_3 + \dots\).