Light and Optics

**1. The Nature of Light — From Lahore Fort to Your Eye**

Light is a transverse wave that belongs to the electromagnetic spectrum. Unlike sound, light does not need a medium — it travels through a vacuum at 3 × 10⁸ m/s. When you see the Badshahi Mosque lit up at night from across Iqbal Park in Lahore, light travels from the floodlights through air into your eyes almost instantly.

Light travels in straight lines (rectilinear propagation). This is why shadows form — opaque objects block light, creating a dark region behind them. A shadow has two parts: the umbra (total shadow) and penumbra (partial shadow). During a solar eclipse visible from Pakistan, the Moon blocks sunlight, casting an umbra on Earth's surface.

**2. Reflection of Light**

When light hits a surface, it bounces back — this is reflection.

Laws of Reflection:

1. The angle of incidence (i) equals the angle of reflection (r): `i = r`
2. The incident ray, reflected ray, and normal (a perpendicular line at the point of incidence) all lie in the same plane.

Types of reflection:

• Regular (specular) reflection: from smooth surfaces like mirrors — produces clear images.
• Diffuse reflection: from rough surfaces like a Karachi bazaar wall — light scatters in all directions.

Plane mirror images are: virtual, upright, laterally inverted, same size as the object, and the same distance behind the mirror as the object is in front.

**3. Refraction of Light**

Refraction occurs when light changes speed as it passes from one medium to another, causing it to bend.

• Light entering a denser medium (air → glass) bends towards the normal and slows down.
• Light entering a less dense medium (glass → air) bends away from the normal and speeds up.

Snell's Law: `n₁ sin(i) = n₂ sin(r)`

Where n is the refractive index. For glass, n ≈ 1.5. For water, n ≈ 1.33.

Refractive index can also be calculated as: `n = speed of light in vacuum ÷ speed of light in medium`

A straw in a glass of *lassi* appears bent at the surface — this is refraction in action.

**4. Total Internal Reflection and Critical Angle**

When light travels from a denser to a less dense medium, increasing the angle of incidence eventually reaches the critical angle (c).

• At the critical angle, the refracted ray travels along the surface (angle of refraction = 90°).
• Beyond the critical angle, total internal reflection occurs — all light is reflected back into the denser medium.

Formula: `sin(c) = 1/n`

Applications: Optical fibres (used in Pakistan's internet backbone connecting Karachi to Islamabad), endoscopes, and bicycle reflectors all use total internal reflection.

**5. Lenses and Image Formation**

Converging (convex) lens: thicker in the middle, brings parallel rays to a **focal point (F)**.

Diverging (concave) lens: thinner in the middle, spreads parallel rays outward.

Key terms:

• Principal axis: straight line through the centre of the lens
• Focal length (f): distance from lens centre to the focal point
• Power of a lens: `P = 1/f` (measured in dioptres, D)

Lens formula: `1/f = 1/v - 1/u` (sign convention: real is positive)

Magnification: `M = image height ÷ object height = v ÷ u`

Real images can be projected on a screen (formed by converging lenses when object is beyond F). Virtual images cannot be projected (formed when object is between F and the lens).

Pakistan connection: Eye doctors across Pakistan prescribe spectacles using lens power in dioptres — a short-sighted student in Lahore might need a -2.0 D diverging lens.

**Exam Strategy**

• Always draw ray diagrams with a ruler and label the normal, angles, and focal points.
• State whether images are real/virtual, upright/inverted, magnified/diminished.
• In refraction problems, identify which medium is denser and which direction light bends.
• For total internal reflection questions, calculate the critical angle first using `sin(c) = 1/n`.
• Remember: refractive index is always ≥ 1 for any medium denser than vacuum.