Light Energy

A. Rectilinear Propagation of Light:

Light travels in straight lines through a homogeneous, isotropic optical medium at a colossal speed of $c = 3 \times 10^8\text{ m/s}$ ($300,000\text{ km/s}$).

• Ray: A narrow straight path of light indicated with an arrow showing direction.
• Beam: A bundle of rays: Parallel beam (searchlights), Convergent beam (focusing on a point), Divergent beam (spreading from a point source).

B. Shadows: Umbra & Penumbra:

• Umbra: The inner region of total darkness behind an opaque object where NO light rays can enter.
• Penumbra: The outer surrounding region of partial darkness where only some light rays reach from an extended light source.

C. Eclipses:

• Solar Eclipse: Occurs on a New Moon day when the Moon passes directly between the Sun and Earth, casting the Moon's shadow onto Earth.
• Lunar Eclipse: Occurs on a Full Moon night when the Earth passes directly between the Sun and Moon, casting Earth's shadow onto the Moon.

A. Terminology:

• Incident Ray ($AO$): The ray of light traveling towards and falling on the reflecting surface.
• Point of Incidence ($O$): The point where the incident ray strikes the surface.
• Normal ($ON$): The imaginary line drawn strictly perpendicular ($90^\circ$) to the reflecting surface at the point of incidence.
• Reflected Ray ($OB$): The ray of light that bounces back into the same medium.
• Angle of Incidence ($\angle i$): Angle between incident ray and normal ($\angle AON$).
• Angle of Reflection ($\angle r$): Angle between reflected ray and normal ($\angle BON$).

B. The Two Laws of Reflection:

1. First Law: The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
2. Second Law: The angle of incidence is strictly equal to the angle of reflection: $$\mathbf{\angle i = \angle r}$$

A. 5 Key Characteristics of Plane Mirror Images:

1. Virtual: Formed behind the mirror by the apparent intersection of produced rays; cannot be captured on a physical screen.
2. Erect (Upright): The image orientation is right-side up.
3. Same Size as Object: Magnification $m = \frac{\text{Image Height } h_i}{\text{Object Height } h_o} = 1$.
4. Equidistant: Object distance in front of mirror equals image distance behind mirror: $$\mathbf{u = v}$$
5. Laterally Inverted: The left side of the object appears as the right side of the image, and vice versa.

B. Lateral Inversion & The Ambulance Design:

Because plane mirrors produce lateral inversion, the word AMBULANCE is painted laterally reversed on the front of emergency medical vehicles so that drivers looking in their rear-view mirrors read the lettering in standard left-to-right orientation!

A. Formula for Number of Images ($n$):

When two plane mirrors are placed inclined at an angle $\theta$:

• At $\theta = 90^\circ$: $n = \frac{360}{90} - 1 = 4 - 1 = \mathbf{3\text{ images}}$.
• At $\theta = 60^\circ$: $n = \frac{360}{60} - 1 = 6 - 1 = \mathbf{5\text{ images}}$.
• At $\theta = 0^\circ$ (Parallel Mirrors): $n = \frac{360}{0} - 1 = \mathbf{\infty \text{ (Infinite Images)}}$!

B. The Periscope:

Consists of a tube containing two plane mirrors inclined at an angle of $45^\circ$ to the tube axis facing each other. Light undergoes two successive $90^\circ$ reflections, enabling observers to see over obstacles or from submerged submarines.

C. The Kaleidoscope:

Consists of three rectangular plane mirrors inclined at $60^\circ$ to each other forming an equilateral prism. Multiple reflections of colored glass fragments create infinitely symmetric hexagonal patterns.