10.2 Optics & Light

Reflection of Light

When light strikes a surface, part of it bounces back. The law of reflection states:

The angle of incidence (θᵢ) equals the angle of reflection (θᵣ), both measured from the normal (the line perpendicular to the surface at the point of incidence).

This law holds for both plane and curved mirrors and is the basis of all mirror imaging. A plane mirror forms a virtual, upright, laterally inverted image the same size as the object, located the same distance behind the mirror as the object is in front.

Refraction and Snell's Law

Refraction is the bending of light as it passes between media of different optical density (different refractive index n). Snell's law is:

n₁ sinθ₁ = n₂ sinθ₂

where n is the refractive index (n = c / v, the ratio of the speed of light in vacuum to its speed in the medium).

• Refractive index of air ≈ 1.0003 (very close to vacuum, n = 1.0000).
• Refractive index of water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.

When light enters a denser medium (higher n) it bends toward the normal; entering a less dense medium it bends away from the normal.

Worked example 1. Light passes from air (n = 1.00) into glass (n = 1.50) at an incidence angle of 30°. Find the refraction angle.

sinθ₂ = (n₁/n₂) sinθ₁ = (1.00/1.50) × sin 30° = 0.667 × 0.5 = 0.333 → θ₂ ≈ 19.5° (bent toward the normal, as expected for entering a denser medium).

Total Internal Reflection & Critical Angle

When light travels from a denser to a less dense medium (e.g., glass to air), beyond a certain critical angle θc it cannot escape and is entirely reflected back. The critical angle is given by:

sin θc = n₂ / n₁ (for n₁ > n₂)

For glass (n = 1.5) to air: sin θc = 1/1.5 = 0.667 → θc ≈ 41.8°.

Total internal reflection (TIR) is the operating principle of optical fibres, which carry data and underpin fibre-optic gyroscopes (FOGs) used in inertial navigation systems on modern fighters. This is a high-yield PAF link.

Lenses and the Lens/Mirror Equation

• Convex (converging) lens — thicker at the centre, converges parallel rays to a real focus. Used in cameras, the eye, and magnifying glasses (when object is inside f).
• Concave (diverging) lens — thinner at the centre, spreads parallel rays; forms only virtual, reduced, upright images.

The lens/mirror equation is:

1/f = 1/v + 1/u

where f is focal length, v image distance, u object distance (all measured from the lens/mirror, with the real-is-positive sign convention). Magnification M = -v/u (the sign indicates image inversion).

Worked example 2. An object is placed 30 cm from a convex lens of focal length 10 cm. Find the image distance.

1/v = 1/f − 1/u = 1/10 − 1/30 = (3 − 1)/30 = 2/30 → v = 15 cm (real, inverted image, on the opposite side).

Snell's Law — Numerical Trap

Worked example 3. A diver underwater (n = 1.33) looks up at a lamp above the surface; the ray from the lamp hits the water surface at 40° to the normal (in air). Find the angle in water.

n₁ sinθ₁ = n₂ sinθ₂ → 1.00 × sin 40° = 1.33 × sinθ₂ → sinθ₂ = 0.643/1.33 = 0.483 → θ₂ ≈ 28.9°. The ray bends toward the normal entering the denser water — consistent with the rule.

Trap: Students often plug in (n₂/n₁) instead of (n₁/n₂). Always start from n₁ sinθ₁ = n₂ sinθ₂ and isolate the unknown; do not memorise a "ratio" without knowing which side is which.

Lens Equation with Magnification

Worked example 4. A 5.0 cm tall object is placed 15 cm from a convex lens of focal length 10 cm. Find the image distance, nature, and magnification.

1/v = 1/f − 1/u = 1/10 − 1/15 = (3 − 2)/30 = 1/30 → v = 30 cm (real, on the opposite side). Magnification M = −v/u = −30/15 = −2. The image is inverted (negative sign) and twice the object size, so image height = 5.0 × 2 = 10 cm.

Critical Angle — Worked Example

Worked example 5. For a glass of refractive index 1.52 in contact with air, find the critical angle.

sin θc = n₂/n₁ = 1.00/1.52 = 0.658 → θc ≈ 41.1°. Any ray inside the glass hitting the boundary at >41.1° is totally internally reflected — the principle keeping light inside an optical fibre.

Common Optics Traps

• "Light-year is a unit of time" — it is a unit of distance (≈9.46 × 10¹⁵ m). Always read the option that says "distance" carefully.
• Normal, not the surface — angles of incidence/reflection are measured from the normal, never from the mirror surface itself.
• Convex mirror = diverging (forms only virtual, reduced images); concave mirror = converging (can form real or virtual images). Do not confuse with lens naming, where convex = converging and concave = diverging — the mirror naming is opposite in effect because it refers to the reflecting surface, not the transmitting shape.
• TIR needs denser → rarer — total internal reflection only occurs when light tries to go from a higher-n to a lower-n medium; it cannot happen going from air into glass.

Light-Year — a Unit of Distance

A light-year is the distance light travels in vacuum in one Julian year (365.25 days):

1 light-year ≈ 9.46 × 10¹⁵ m ≈ 63000 AU

It is a unit of distance, not time — a classic PAF trap. The nearest star system, Alpha Centauri, is about 4.37 light-years away.

Aviation Optics Links

• Head-up displays (HUDs) use a collimating lens to project instrument data onto the windscreen so the pilot can read it without looking inside the cockpit.
• Fibre-optic gyroscopes use TIR in fibre loops to sense rotation — central to inertial navigation.
• Canopy refraction slightly shifts the apparent position of external objects — a real concern for aerial refuelling and formation flying.