Worked examples (Lesson 2)

Example 2.1 — Intensity comparison. A 5 mW laser beam has a cross-section of radius 1 mm. An ordinary point source of the same power radiates in all directions. Compare their intensities at 10 m. Laser: I = P/A = 5 × 10⁻³ / (π × (10⁻³)²) = 1.6 × 10³ W/m². Point source at 10 m: I = P/(4πr²) = 5 × 10⁻³/(4π × 100) = 4.0 × 10⁻⁶ W/m². The laser's intensity is about 4 × 10⁸ times greater.

Example 2.2 — Moon ranging. A pulse sent to the Moon's reflector takes how long to come back? Distance 3.84 × 10⁸ m: t = 2d/c = 2 × 3.84 × 10⁸/3 × 10⁸ = 2.56 s. If the time can be measured to 1 nanosecond, the distance is known to 15 cm (2d = ct).

Example 2.3 — Inverse-square law. The intensity of an ordinary lamp at 1 m is 400 W/m². At 4 m it is 400/16 = 25 W/m². A laser beam's intensity at 4 m is unchanged.