Light Energy

1. First Law: The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
   2. Second Law (Snell's Law): The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is a constant for a given pair of media and for a given color of light:
   

$$\mathbf{\frac{\sin i}{\sin r} = \mu \quad (\text{Refractive Index})}$$

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Apply the formula: $\mu = \frac{c}{v}$.

$$\mu = \frac{3 \times 10^8\text{ m/s}}{2 \times 10^8\text{ m/s}} = \frac{3}{2} = \mathbf{1.5}$$

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The refractive index of the glass is $1.5$ (pure dimensionless number).

• Lateral Displacement: The perpendicular distance between the original path of the incident light ray and the emergent ray emerging from a parallel-sided rectangular glass slab.
• Factors Affecting Lateral Displacement:
1. Thickness of the Glass Slab ($t$): Greater thickness produces a larger lateral displacement ($d \propto t$).
2. Angle of Incidence ($i$): Higher angle of incidence increases lateral displacement.
3. Refractive Index ($\mu$): Higher optical density increases lateral displacement.

A ray of light passes undeviated under two specific conditions:
1. Normal Incidence: When the light ray strikes the boundary perpendicularly at an angle of incidence $\angle i = 0^{\circ}$.
2. Equal Refractive Indices: When both optical media have the exact same refractive index ($\mu_1 = \mu_2$), meaning the speed of light is identical in both media.

• The rays of sunlight traveling toward Earth are essentially parallel rays of light.
• A convex lens is a converging lens that refracts all incoming parallel rays and focuses them onto a single point: its Principal Focus ($F$).
• All the concentrated thermal and radiant energy of the sunlight is focused into an intense microscopic spot, generating extreme heat sufficient to ignite dry paper.

• Violet light deviates the MOST.
• Red light deviates the LEAST.
• Scientific Reason:
In a vacuum, all colors travel at the same speed ($c$). But in a dense glass medium, different wavelengths travel at different speeds.
Red light has the longest wavelength and travels fastest in glass, experiencing the lowest refractive index, and bends the least.
Violet light has the shortest wavelength and travels slowest in glass, experiencing the highest refractive index, and is bent most sharply.

1. Intersection: A Real image is formed by the actual physical intersection of refracted light rays; A Virtual image is formed when refracted rays diverge and appear to meet only when extended backward.
   2. Screen Capture: A real image can be captured on a screen; A virtual image cannot be projected onto a screen.
   3. Orientation: Real images are always inverted; Virtual images are always erect (upright).

Apply the Prism Relation: $A + \delta = i + e$.

$$60^{\circ} + \delta = 48^{\circ} + 42^{\circ}$$

$$60^{\circ} + \delta = 90^{\circ}$$

$$\delta = 90^{\circ} - 60^{\circ} = \mathbf{30^{\circ}}$$

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The angle of deviation is $30^{\circ}$.