Complete Light for CDS Exam Physics for CDS - AFCAT Physics

Light and Its Properties

Light enables vision by making objects visible. It is the cause for us to see and perceive objects around us. Light is essential for the sense of sight; without it, objects cannot be seen.

Types of Objects: Luminous and Non-Luminous

Objects are categorized based on their ability to emit light. Luminous objects emit their own light, while non-luminous objects do not and are visible only when illuminated by luminous sources.

• Luminous Objects: Emit their own light (e.g., bulb, tube light, Sun).
• Non-Luminous Objects: Do not emit light; visible due to reflected light…

Light and Its Properties

Light enables vision by making objects visible. It is the cause for us to see and perceive objects around us. Light is essential for the sense of sight; without it, objects cannot be seen.

Types of Objects: Luminous and Non-Luminous

Objects are categorized based on their ability to emit light. Luminous objects emit their own light, while non-luminous objects do not and are visible only when illuminated by luminous sources.

• Luminous Objects: Emit their own light (e.g., bulb, tube light, Sun).
• Non-Luminous Objects: Do not emit light; visible due to reflected light (e.g., table, chair).

Nature of Light and Related Theories

Light exhibits dual nature, showing both wave and particle characteristics. Various theories and scientists have explained these aspects.

• Dual Nature: Light behaves as both a wave and a particle.
• Wave Nature Explained By: Reflection, refraction, diffraction, scattering, interference, total internal reflection (TIR).
• Particle Nature Explained By: Compton effect, photon effect (not in syllabus).
• Key Contributors:
  • Particle theory: Newton
  • Wave theory: Huygens
  • Interference: Thomas Young
  • Electromagnetic theory: Maxwell
  • Quantum theory: Max Planck
  • Photon phenomenon: Einstein

Mirrors: Plane and Spherical

Mirrors are classified as plane or spherical, each with distinct properties and uses.

• Plane Mirror: Flat surface, one side polished (often with silver or zinc oxide), other side shining (reflecting surface).
• Spherical Mirror: Curved surface, can be concave (polished outside, converging) or convex (polished inside, diverging).

Properties of Plane Mirror

Plane mirrors form images with specific characteristics:

• Laterally Inverted Image: Right appears left and vice versa (e.g., ambulance lettering).
• Virtual and Erect Image: Image appears upright and cannot be projected on a screen.
• Minimum Mirror Height: To see full image, mirror height must be at least half the object's height.
• Relative Velocity: If object moves towards mirror with velocity $v$, image approaches with $2v$.

Applications of Plane Mirror

Plane mirrors are used in various instruments:

• Periscope: Uses two plane mirrors at $45^\circ$ for viewing over obstacles (e.g., in submarines).
• Kaleidoscope: Uses three plane mirrors at $60^\circ$ to create multiple reflections and patterns.

Spherical Mirrors: Concave and Convex

Spherical mirrors are sections of a sphere and are of two types:

• Concave Mirror: Polished outside, converging mirror.
• Convex Mirror: Polished inside, diverging mirror.

Key Terms

• Pole (P): Center of mirror surface.
• Principal Axis: Line passing through pole and center of curvature.
• Center of Curvature (C): Center of the sphere from which mirror is cut.
• Focus (F): Point where parallel rays converge/diverge.
• Radius of Curvature (R): Distance from pole to center of curvature.
• Focal Length (f): Distance from pole to focus; $f = R/2$.

Image Formation by Mirrors

Image formation depends on object position and mirror type. Four main rules for ray diagrams:

• A ray parallel to principal axis passes through focus after reflection.
• A ray passing through focus emerges parallel to principal axis.
• A ray striking the pole reflects at equal angle.
• A ray passing through center of curvature reflects back on itself.

Types of Images

• Real and Inverted: Formed below principal axis, can be projected.
• Virtual and Erect: Formed above principal axis, cannot be projected.

Concave Mirror Cases

• Concave mirror forms real, inverted images in 90% cases; only between F and P does it form virtual, erect image.

Convex Mirror Cases

• Only two cases:
  • Object at infinity: Image at focus, highly diminished, virtual, erect.
  • Object between infinity and pole: Image between P and F, diminished, virtual, erect.

Convex mirror always forms virtual, erect images.

Mirror Formula, Magnification, and Sign Conventions

Mathematical relationships for mirrors are essential for solving numerical problems.

• Mirror Formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
• Magnification: $m = -\frac{v}{u}$ and $m = \frac{h_2}{h_1}$
  • $h_1$ = object height, $h_2$ = image height

Sign Conventions:

• Distances measured towards mirror (left) are negative.
• Heights above principal axis are positive; below are negative.
• For real, inverted images (concave): $u$, $v$, $f$ negative.
• For virtual, erect images: $v$, $f$ positive.

Reflection and Refraction of Light

Reflection is the bouncing back of light from a surface; refraction is the bending of light when it passes from one medium to another.

Laws of Reflection

• Angle of incidence equals angle of reflection.
• Incident ray, reflected ray, and normal lie in the same plane.

Laws of Refraction

• Light bends towards normal when moving from rarer to denser medium.
• Light bends away from normal when moving from denser to rarer medium.

Refractive Index ($\mu$):

• $\mu = \frac{\text{speed of light in vacuum}}{\text{speed of light in medium}} = \frac{c}{v}$
• Also, $\mu = \frac{\lambda_{\text{vacuum}}}{\lambda_{\text{medium}}}$

Factors Affecting Refractive Index:

• Nature of medium
• Wavelength of light
• Nature of surrounding medium
• Temperature

Total Internal Reflection (TIR)

TIR occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle, causing all light to reflect back into the denser medium.

• Conditions for TIR:
  • Light must travel from denser to rarer medium.
  • Angle of incidence must exceed the critical angle (where angle of refraction is $90^\circ$).

Applications:

• Mirage formation (illusion of water on road/desert)
• Shining of diamond
• Optical fiber cables

Dispersion and Scattering of Light

Dispersion is the splitting of white light into seven colors when passed through a prism. Scattering is the spreading of light in different directions due to particles.

• Order of Colors (VIBGYOR): Violet, Indigo, Blue, Green, Yellow, Orange, Red
• Deflection: Violet is most deflected (minimum wavelength), red is least deflected (maximum wavelength).
• Scattering Intensity: Inversely proportional to $\lambda^4$ (Rayleigh scattering).
  • Red scatters least, blue scatters most.

Applications:

• Red used for danger signals (least scattered).
• Sky appears blue due to maximum scattering of blue light.
• Clouds appear white/bluish; sea appears blue due to scattering.

Rainbow Formation and Interference of Light

Rainbows are formed due to dispersion, refraction, and TIR in water droplets.

• Primary Rainbow: One TIR, two refractions.
• Secondary Rainbow: Two TIRs, two refractions.

Interference: Superimposition of light waves leading to constructive (amplitude increases) or destructive (amplitude decreases) patterns.

• Applications: Soap bubbles, oil films on water.

Lenses: Types, Image Formation, and Power

Lenses are of two types: concave (diverging) and convex (converging). Rules for image formation are similar to mirrors.

• Concave Lens: Similar to convex mirror, always forms virtual, erect images; focal length is negative.
• Convex Lens: Similar to concave mirror, forms real, inverted images (except in one case); focal length is positive.

Lens Formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Magnification for Lens: $m = \frac{h_2}{h_1} = \frac{v}{u}$

Power of Lens: $P = 1/f$ (f in meters)

• For concave lens, $f$ is negative, so power is negative.

Defects of Vision and Their Correction

Human eye defects include myopia, hypermetropia, presbyopia, and astigmatism.

• Myopia (Short-sightedness): Can see near objects, not distant; image forms before retina. Corrected with concave lens. Causes: increased curvature, decreased focal length, increased lens power.
• Hypermetropia (Long-sightedness): Can see distant objects, not near; image forms beyond retina. Corrected with convex lens. Causes: decreased curvature, increased focal length, decreased lens power.
• Presbyopia: Age-related; difficulty seeing both near and far objects. Corrected with bifocal lenses (combination of concave and convex).
• Astigmatism: Due to irregular curvature or opacity (e.g., cataract); corrected as per cause.

Color of Objects Under Different Lights

The color an object appears depends on the color of light it reflects. A table summarizes the appearance of objects under different colored lights:

• Same color object in same color light appears as that color; in other colors, appears black.
• White objects reflect all colors; black objects absorb all colors.

This table is important for quick recall in exams.