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Law of Reflection

CSCA Law of Reflection 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 Reflection

Law of Reflection

1. Conceptual Definition

The Law of Reflection is the cornerstone of geometrical optics, describing how light changes direction when it encounters a smooth interface (like a mirror). Though simple, it is the foundation for analyzing complex optical systems (e.g., periscopes, optical fibers, reflecting telescopes).

2. Core Law

* **Coplanarity**: The incident ray, the reflected ray, and the normal lie in the same plane.

* **Equality of Angles**: The angle of reflection equals the angle of incidence.

$$\theta_r = \theta_i$$

**Key Definitions (Common Pitfalls)**:

* **Normal**: An imaginary line drawn through the point of incidence, **perpendicular to the mirror surface**. It is the reference for all angle measurements.

* **Angle of Incidence/Reflection**: The angle between the ray and the **Normal**, **NEVER** the angle with the mirror surface.

3. Key Exam Points

#### A. Principle of Reversibility

If a light ray is sent along the path of the reflected ray (reversed direction), it will reflect back along the path of the original incident ray.

#### B. Rotation Effect (Double Angle Rule)

This is a high-frequency topic in CSCA exams.

**Conclusion**: If the incident ray is fixed and the plane mirror rotates by an angle $\alpha$, the reflected ray will rotate by an angle of **$2\alpha$**.

* **Derivation**: Mirror rotates $\alpha$ $\rightarrow$ Normal rotates $\alpha$ $\rightarrow$ Angle of incidence changes by $\alpha$ $\rightarrow$ Angle of reflection changes by $\alpha$ $\rightarrow$ Total change in reflected ray is $2\alpha$.

4. Typical Examples

**Example 1: Basic Angle Calculation (Trap Question)**

A light ray strikes a plane mirror at an angle of $30^\circ$ to the mirror surface. Find the angle between the reflected ray and the incident ray.

* **Analysis**: The question gives the angle with the *mirror*, not the angle of incidence.

* **Steps**:

1. Calculate Angle of Incidence: $\theta_i = 90^\circ - 30^\circ = 60^\circ$.

2. Calculate Angle of Reflection: $\theta_r = 60^\circ$.

3. Calculate Total Angle: $\theta_{total} = \theta_i + \theta_r = 120^\circ$.

**Example 2: Optical Lever Principle**

A laser beam strikes a horizontal plane mirror, forming a spot on a wall $L=10m$ away. If the mirror rotates by $3^\circ$ (small angle), how far does the spot move on the wall?

* **Analysis**:

1. Mirror rotation $\alpha = 3^\circ$.

2. According to the Double Angle Rule, the reflected ray rotates by $\theta = 2\alpha = 6^\circ$.

3. Use geometry to calculate the distance.

* **Calculation**:

$$d \approx L \cdot \tan(2\alpha) \approx L \cdot \tan(6^\circ)$$

$$d \approx 10 \cdot 0.105 = 1.05m$$

* **Conclusion**: The spot moves approximately $1.05m$. This demonstrates how reflection can amplify small rotations (Optical Lever).