Light & Optics

Light is an electromagnetic wave; speed in vacuum = 3 × 10⁸ m/s. It travels in straight lines (rectilinear propagation).

Reflection laws:

1. Angle of incidence = angle of reflection.
2. Incident ray, reflected ray and normal lie in the same plane.

Plane mirror image:

• Same size as object.
• Equally distant behind the mirror as the object is in front.
• Virtual (cannot be projected on a screen).
• Laterally inverted (left ↔ right swap).

Spherical mirrors:

• Concave (converging): focus is real, in front of the mirror. Used in shaving mirrors (close objects appear larger), torches, solar concentrators.
• Convex (diverging): focus is virtual, behind the mirror. Used in vehicle rear-view mirrors (wider field of view). Image is always virtual, erect, smaller than object.

Mirror formula: 1/v + 1/u = 1/f, where u = object distance, v = image distance, f = focal length. Sign convention: distances measured from pole; positive in the direction of incident light's opposite (Cartesian convention).

Magnification: m = h_image / h_object = −v/u.

Refraction: bending of light when it passes from one medium to another.

• Light entering a denser medium (air → water, air → glass) bends towards the normal.
• Entering a rarer medium, it bends away.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂, where n is refractive index.

Refractive index: n = (speed of light in vacuum) / (speed in medium). Water n ≈ 1.33, glass n ≈ 1.5.

Total internal reflection: when light goes from denser to rarer medium and the angle exceeds a critical angle, it reflects entirely. The basis for optical fibres and the sparkle of diamonds.

Lenses:

• Convex (converging): thicker in middle. Magnifying glass, camera, hyperopia correction.
• Concave (diverging): thinner in middle. Myopia (short-sight) correction.
• Lens formula: 1/v − 1/u = 1/f.
• Power = 1/f (in metres). Unit: dioptre (D). Convex: positive D; concave: negative D.

Example 1 — Mirror image distance:
You stand 2 m from a plane mirror. How far away is your image?
Method: image is 2 m behind the mirror → total distance from you = 4 m.

Example 2 — Refraction:
Light enters water (n = 1.33) from air at 30°. Refraction angle?
Method: 1 × sin 30° = 1.33 × sin θ_r → sin θ_r = 0.5/1.33 ≈ 0.376 → θ_r ≈ 22°.

Example 3 — Power of a lens:
A convex lens has focal length 25 cm. Find its power.
Method: P = 1/f (in m) = 1/0.25 = +4 D.

Human eye:

• The cornea + lens form an image on the retina (a real, inverted, smaller image).
• Iris controls light entry (acts as aperture).
• The retina has rods (light intensity, B&W vision) and cones (colour).
• Three cone types detect red, green, blue.

Defects of vision:

• Myopia (short sight): distant objects blurred; image forms in front of retina. Correct with concave lens.
• Hyperopia (long sight): nearby objects blurred; image forms behind retina. Correct with convex lens.
• Presbyopia: age-related loss of accommodation; correct with bifocals.
• Astigmatism: uneven curvature of cornea; correct with cylindrical lens.

Dispersion: a prism splits white light into seven colours — VIBGYOR. Violet bends most (shorter wavelength), red bends least.

Rainbow: water droplets act as prisms + mirrors. Sunlight is dispersed, internally reflected once in each drop, then refracted out at ~42°. A double rainbow has a second arc with reversed colour order due to two internal reflections.

Why is the sky blue? Rayleigh scattering: shorter wavelengths (blue) scatter more than longer (red). At sunset, light passes through more atmosphere, blue scatters away, red remains.

Speed-of-light facts:

• Light from the Sun reaches Earth in ~8 minutes 20 seconds.
• Light from the nearest star (Proxima Centauri) takes 4.2 years.
• 1 light-year ≈ 9.46 × 10¹⁵ m.