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• Reflection is when light bounces back from a polished surface, like a mirror

Laws of Reflection

• Angle of incidence equals the angle of reflection (i = r)
• The incident ray, reflected ray, and normal all lie in the same plane

Spherical Mirrors

• Concave mirrors converge light

• Convex mirrors diverge light

• Pole: The center point of the spherical mirror's reflecting surface

• Center of Curvature: The center of the sphere which the mirror is a part

• Principle Axis: The line joining the pole and the center of curvature, normal to the mirror at the pole

• Radius of Curvature: The distance between the pole and the center of curvature (PC)

Principle Focus (F) and Focal Length (f)

• For Concave mirrors parallel rays converge at the focus F
• For Convex mirrors parallel rays appear to diverge from the Focus F

Image Formation - Concave Mirror

• Object at infinity: Image at the focus, highly diminished and point-sized, real and inverted
• Object beyond C: Image between F and C, diminished, real and inverted
• Object at C: Image at C, same size, real and inverted
• Object between C and F: Image beyond C, enlarged, real and inverted
• Object at F: Image at infinity, highly enlarged, real and inverted
• Object between the pole and F: Image behind the mirror, enlarged, virtual and erect

Image Formation - Convex Mirror

• Object at infinity: Image at F, virtual, erect, highly diminished, point size
• Object at finite distance: Image between F and P, virtual, erect, diminished, upright

Concave Mirror Uses

• Can concentrate sunlight to produce heat in solar furnaces

Convex Mirror Uses

• Used as rear-view mirrors, provides upright/erect images with a wider field of view

Sign Convention

• All distances are measured from the pole
• Distances to the right (along +x axis) are positive
• Distances to the left (along -x axis) are negative
• Heights above the axis are positive (h=+ve)
• Heights below the axis are negative (h=-ve)

Mirror Formula and Magnification

• Mirror formula: 1/f = 1/u + 1/v
• Magnification (m) = height of image (hi) / height of object (ho) = -v/u
• f is positive for concave mirrors

Spherical Lenses

• Convex lens: Thicker in the middle
• Concave lens: Thinner in the middle

Convex Lens Image Formation

• Object at infinity: Image at F2, real, inverted, and highly diminished
• Object between infinity and 2F1: Image between F2 and 2F2, real, inverted, and diminished
• Object at 2F1: Image at 2F2, real, inverted, and same size
• Object between F1 and 2F1: Image beyond 2F2, real, inverted, and enlarged
• Object at F1: Image at infinity, real, inverted, and enlarged
• Object between F1 and optical center (O): Image on the same side, virtual, erect, and enlarged

Concave lens

• Always Erect/Upright, Diminished

Refraction of Light

• Light bends when traveling from one medium to another
• Rarer to denser: Bends towards the normal
• Denser to rarer: Bends away from the normal
• In absolute refractive index, the first medium is air, and the second is any other medium

Absolute Refractive Index

• Formula: n = c/v, where c is the of light in a vacuum and v is the of light in the medium
• Refractive Index of water with respect to Air (nwa): nw/na = va/vw

Refraction Through a Glass Slab

• The emergent ray is parallel to the incident ray

Laws of Refraction

• The incident ray, normal, and refracted ray lie in the same plane
• Snell's Law: 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. (sin(i) / sin(r) = constant)
• Formula also represented as: n1sin(i1) = n2sin(r2)

No Bending conditions

• Normal incidence (i = 0, r = 0)
• No medium change or no change in refractive index

Image Formation - Concave Lens

• Object at infinity: Image at F1, virtual, erect, highly diminished (point size)
• Object at finite distance: Image between F1 and optical center O, virtual, erect, diminished

Sign Convention, Lens Formula & Magnification

• All distances are measured from the optical center
• Lens formula: 1/f = 1/v - 1/u
• Magnification (m) = hi/ho = v/u
• f is positive for convex lens
• f is negative for concave lens

Power of a Lens

• Ability to converge or diverge rays of light
• Defined as the reciprocal of focal length (P = 1/f)
• Unit: Diopters (D)
• f should be in meters
• For a combination of lenses: P = P1 + P2

The Human Eye

• Eyeball: Approximately spherical, diameter 2-3cm

• Cornea: Thin, transparent, bulging membrane where most of the refraction occurs, protects from dust and germs

• Iris: Controls the size of the pupil

• Pupil: Regulates the amount of light entering the eye

• Crystalline lens: Convex lens, flexible focal length to form real and inverted image

• Ciliary Muscles: Adjust the focal length of the eye lens

• Retina: Screen where real, inverted image is formed, contains light-sensitive cells (rods and cones)

  • Rods: Vision in low light (light intensity)
  • Cones: Vision in high light and color vision

Power of Accommodation

• Ability of the eye lens to adjust its focal length

Defects of the Eye

• Myopia (Nearsightedness): Can see nearby objects clearly, cannot see distant objects
  • Image of distant object formed in front of the retina
  • Caused by excessive curvature of the lens, lens is thick, elongation of the eyeball
  • Corrected using a concave lens
• Hypermetropia (Farsightedness): Can see distant objects clearly, cannot see nearby objects
  • Image of nearby objects formed behind the retina
  • Caused by focal length of the lens too long, eyeball too small
  • Corrected using a convex lens
• Presbyopia: Difficulty seeing nearby objects clearly, and declining flexibility of eye lens
  • Corrected using bi-focal lenses

Refraction of Light & Deviation Through a Prism

• A prism bends a ray of light towards its base
• White is made of seven colors.
• Angle of Deviation (D) different for different colors of light
• Violet bends the most

Refraction of White Light (Sunlight) Through a Prism

• Dispersion: Splitting of white light into its component colors (spectrum)
• Spectrum: The band of color components of light (obtained on a screen)

Atmospheric Refraction

• Density of air decreases with height, causing refraction

Rainbow Formation

• Dispersion + Refraction + Reflection

Advance Sunrise and Delay Sunset

• The sun is visible for about 2 minutes before actual sunrise and 2 minutes after actual sunset due to atmospheric refraction

Twinkling of Stars

• Stars appear to twinkle because of varying atmospheric conditions
• Planets do not twinkle because they are closer and behave as extended sources of liight

Color of the Sky

• Molecules in the air scatter blue light more than red, leading to the sky's blue appearance

Tyndall Effect

• Phenomenon of scattering of light by colloidal particles

Electric Charge

• Two types of charges exist
• Like charges repel, unlike charges attract
• SI unit of charge is the Coulomb (C)
• 1e = 1.6 x 10^-19 C

Electric Current

• Rate of flow of electric charge, direction opposite to electron flow
• SI unit is the Ampere (A)

Potential Difference (Voltage)

• Work done to move a unit charge from one point to another, measured in Volts (V)

Resistance

• Obstruction to the flow of charge, measured in Ohms (Ω)

Factors Affecting Resistance

• Length of conductor (R ∝ l)
• Area of cross-section (R ∝ 1/A)
• Material of the conductor (resistivity)
• Temperature (for most materials, resistance increases with temperature)

Ohm's Law

• Potential difference is directly proportional to current at constant temperature (V = IR)

Combinations of Resistors

• Series: Total resistance is the sum of individual resistances
• Parallel: Reciprocal of total resistance is the sum of reciprocals of individual resistances

Electric Power

• Rate at which electrical energy is consumed, measured in Watts (W)
• P = VI = I^2 * R = V^2 / R

Electric Energy (E)

• Generally measured in Joule (J)
• Commercial Unit 1kWh = 3.6 x 10^6 J

Heating Effect of Electric Current

• Heat = i^2 * Rt (Joule's Law)

Electric Fuse

• Safety device to prevent short circuits and overloading

Magnetism

• Objects attract iron, nickel, cobalt

Magnetic Field

• Space surrounding magnet where its force is felt

Magnetic Field Lines

• Imaginary lines showing magnetic field direction
• Closer lines indicate stronger field

Current-Carrying Conductor in Magnetic Field

• Experiences a force

Fleming's Left-Hand Rule

• Determines the direction of force on current-carrying conductor in the magnetic field

Electromagnets

• Temporary magnets created by electric current