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Law of Refraction

CSCA Law of Refraction study guide organized around the publicly available CSCA syllabus. Practice Physics questions on aicsca.com.

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Topic: Optics > Geometrical Optics > Law of Refraction

Law of Refraction (Snell's Law)

1. Conceptual Definition

The phenomenon where the direction of light changes when it passes **obliquely** from one medium into another. It is the basis for lenses, mirages, and fiber optics.

2. Core Law

#### A. Snell's Law

This is the **single most important formula** for refraction problems. Memorize the product form to avoid fraction errors:

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

* $n_1, n_2$: **Absolute refractive indices** of the two media.

* $\theta_1, \theta_2$: Angles relative to the **Normal** (Angle of Incidence and Refraction, respectively).

#### B. Refractive Index

A measure of how much a medium slows down light.

* **Definition**: $$n = \frac{c}{v}$$

* $c$: Speed of light in vacuum ($3.0 \times 10^8 m/s$).

* $v$: Speed of light in the medium.

* **Rule**: Higher $n$ means slower light speed (**Optically Denser**); Lower $n$ means faster light speed (**Optically Rarer**).

3. Bending Rules

1. **Rare $\rightarrow$ Dense** ($n_1 < n_2$, e.g., Air to Water): Light slows down, ray bends **Towards the Normal** ($\theta_2 < \theta_1$).

2. **Dense $\rightarrow$ Rare** ($n_1 > n_2$, e.g., Water to Air): Light speeds up, ray bends **Away from the Normal** ($\theta_2 > \theta_1$).

* **Warning**: Always check for **Total Internal Reflection** (if $\theta_1 > \theta_c$) in this case.

4. Typical Models

#### Model 1: Apparent Depth

When observing an underwater object vertically from air, the object appears shallower than it actually is.

* **Formula**: $$h_{apparent} \approx \frac{h_{real}}{n}$$

* $h_{real}$: Actual depth.

* $n$: Refractive index of water (assuming observer is in air, $n_{air}\approx 1$).

#### Model 2: Parallel Glass Slab

When light passes through a parallel glass slab, the emergent ray is **parallel** to the incident ray but undergoes a **Lateral Displacement**.

5. Problem Solving Steps

1. **Draw Normal**: This is the reference for all angles.

2. **Identify Media**: Define which is side 1 (Incident) and side 2 (Refracted).

3. **Equation**: Substitute directly into $n_1 \sin\theta_1 = n_2 \sin\theta_2$.

4. **Calculator**: Ensure your calculator is in "Degree Mode (DEG)".