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Light: Reflection and Refraction

• Light reflection refers to the phenomenon where light bounces back from a polished surface.
• The angle of incidence (∠i) equals the angle of reflection (∠r).
• The incident ray, reflected ray, and the normal all lie in the same plane.

Spherical Mirrors

• Concave mirrors are converging mirrors.
• Convex mirrors are diverging mirrors.
• The pole (P) is the midpoint on the mirror surface.
• The center of curvature (C) is the center of the sphere from which the mirror is cut.
• The principal axis joins 'P' and 'C'.
• The radius of curvature is the distance between 'P' and 'C'.
• The focal length (f) is the distance between 'P' and 'F' (focus).
• 'F' is the center of 'P' and 'C'; therefore, R = 2f.

Image Formation Rules

• At least two rays are required to form an image.
• Real images are formed when rays actually meet.
• Virtual images are formed where rays appear to meet.
• Rays parallel to the principal axis pass through 'F' after reflection in the case of a concave mirror.
• Rays passing through 'F' will become parallel to the principal axis after reflection from a concave mirror.
• Rays passing through 'C' will reflect back along the same path.
• When a ray is incident at 'P', ∠i = ∠r, the principal axis behaves as the normal.

Image Formation by Concave Mirror

• An object at infinity forms a real, inverted, point-sized, and highly diminished image at 'F'.
• An object beyond 'C' forms a real, inverted, and diminished image between 'F' and 'C'.
• An object at 'C' forms a real, inverted image of the same size at 'C'.
• An object between 'C' and 'F' forms a real, inverted, and bigger image beyond 'C'.
• An object at 'F' forms a real, inverted, highly enlarged image at infinity.
• An object between 'P' and 'F' forms a virtual, erect, and enlarged image behind the mirror.
• Real images are inverted, and virtual images are erect.

Image Formation by Convex Mirror

• An object at infinity forms a virtual, erect, point-sized image behind the mirror at 'F'.
• An object between infinity and 'P' forms a virtual, erect, diminished image between 'P' and 'F' behind the mirror.

Magnification

• Magnification indicates how large or small an image is with respect to the object.
• Magnification (m) = (height of image (hi)) / (height of object (ho)) = -v/u.
• A positive 'm' indicates a virtual image; a negative 'm' indicates a real image.

Sign Convention

• All distances are measured from the pole 'P'.
• 'u' is always negative.
• For convex mirrors, f is positive.
• For concave mirrors, f is negative.
• The mirror formula is 1/f = 1/v + 1/u.

Uses of Mirrors

• Concave mirrors are used in torches, headlights, shaving mirrors, and dentist mirrors because they produce enlarged images.
• Convex mirrors are used as rearview mirrors because they produce erect and small images, allowing for a wide view.

Spherical Lenses

• Spherical lenses include convex (converging) and concave (diverging) lenses.
• C represents the center of curvature, F the principal focus, and f the focal length.

Image Formation: Rules (Lenses)

• Rays passing through the lens from F1 to F2

Image Formation by Convex Lens

• An object at infinity forms a real, inverted, highly diminished (point-sized) image at 'F2'.
• An object beyond '2F1' forms a real, inverted, and diminished image between 'F2' and '2F2'.
• An object at '2F1' forms a real, inverted image of the same size at '2F2'.
• An object between 'F1' and '2F1' forms a real, inverted, and enlarged image beyond '2F2'.
• An object at 'F1' forms a real, inverted, and highly enlarged image at infinity.
• An object between 'F1' and 'O' (optical center) forms a virtual, erect, and enlarged image on the same side of the lens as the object.

Image Formation by Concave Lens

• An object at infinity forms a virtual, erect, and highly diminished image at 'F1'.

Important Notes (Lenses)

• Spherical lenses have two focuses.
• All distances are measured from the optical center 'O.'
• The lens formula is 1/f = 1/v - 1/u.
• Magnification (m) = hi/ho = v/u; signs are the same as for mirrors.

Power of a Lens

• Power is the degree of convergence and divergence of a lens.
• The SI unit is Dioptre (D), where D = m⁻¹, and P = 1/f.
• Concave lenses have negative power (-ve); convex lenses have positive power (+ve).

Refraction: Bending of Light

• Refraction occurs due to a change in medium, which leads to a change in the speed of light.
• The refractive index (RI) indicates the density of a medium; RI of 2nd medium w.r.t 1: n12 = n2/n1.
• Higher RI means higher density and a slower speed of light.
• The absolute refractive index assumes one medium is air, thus n = 1; c = 3 x 108 m/s.
• The refractive index of glass is approximately 1.5; of water, it's approximately 1.33.

Laws of Refraction

• The incident ray, refracted ray, and normal all lie in the same plane.
• The ratio of the sine of the angle of incidence to the sine of the angle of refraction remains constant for a given pair of media.

Refraction Through a Glass Slab

• The incident ray is parallel to the emergent ray.
• The angle of incidence (∠i) equals the angle of emergence (∠e).

The Human Eye

• Cornea: Thin, transparent outer membrane that refracts light entering the eye.
• Iris: Controls the size of the pupil.
• Pupil: Controls the amount of light entering the eye.
• Crystalline Lens: Adjusts to see objects at different distances and makes real/inverted images.
• Ciliary Muscles: Changes the curvature of the eye lens.
• Retina: Screen where the image is formed; contains cells that generate electrical signals.
• Optic Nerve: Sends signals to the brain.
• Aqueous Humor: Provides nutrition and support.
• Vitreous Humor: Provides support between the lens and retina.

Power of Accommodation

• Is the ability of the eye to change its focal length.
• When focusing on closer objects, ciliary muscles contract, the lens gets thicker (curvature increases), and the focal length decreases (power increases).
• When focusing on farther objects, ciliary muscles relax, the lens gets thinner (curvature decreases), and the focal length increases (power decreases).
• A normal human eye can see far objects as far as infinity.

Defects of Vision

• Myopia (nearsightedness): Far point is less than infinity; corrected using a concave lens.
• Hypermetropia (farsightedness): Near point is more than 25cm; corrected using a convex lens.
• Presbyopia: Inability to see both near and far objects, often age-related; corrected using bifocal lenses.
• Cataract: Lens becomes opaque and milky, leading to partial or complete vision loss; treated with surgery

Refraction Through a Prism

• A prism is a transparent refracting medium with triangular and rectangular surfaces
• White light splits into seven colors (VIBGYOR) when passed through a prism which is dispersion.
• Violet bends the most, and red bends the least

Rainbow Formation

• Rainbows are formed due to refraction, dispersion, and total internal reflection.
• The sun should be behind the observer and the rainbow in front

Atmospheric Refraction

• Atmospheric refraction occurs because different layers of the atmosphere have different densities.
• Layers closer to the earth have higher densities.

Twinkling of Stars

• Stars appear to twinkle due to variations in atmospheric layers.
• Planets do not twinkle because they are closer and behave as extended sources of light.

Tyndall Effect/Scattering of Light

• Tyndall effect is the scattering of light by heterogeneous colloidal particles.
• The color of scattered light depends on the size of the particles
• Skies are blue because molecules of air and other fine particles scatter blue light more strongly and red during sunset because the the atmosphere scatters away most blue and green light.
• Without an atmosphere, the sky would appear dark.
• Danger and stop signs are red because the particles of fog and smoke scatter red light the least.

Electricity

• Electric Charge: Q, SI unit: Coulomb (C)
  • Charge of an electron (e): 1.6x10-19 C
• Electric Current: I, SI unit: Ampere (A)
  • 1 Ampere = 1 Coulomb/second
  • Defined as the amount of charge flowing through a conductor in time t:
  • I = Q/t, Q = It
  • Electric current is measured using Ammeter

Ohm Law

• V (Voltage) = I (Current) R (Resistance
• Resistance: R, an obstructio to electric flow. SI unit: Ohm (Ω).

Important formulas

• Resistance formula : R = ρL/A
• Where L = Length
• Where A = Area
• Where ρ = resistivity

Factors affecting Resistance:

Nature of material: good or bad conductors Length of conductor: R ∝ L Area of cross-section: R ∝ 1/A

Power and Energy

• Electric Power: P = VI or P = I2R or P = V2/R, SI unit: Watt (W)
• Electrical Energy: E = Pt unit is Joule

Electrical elements A cell

• Combination of cells is called a battery Switch closed
• Switch open

Heating effects

• Heating effect formula : H = IRt