In geometrical optics, the angle of incidence is defined as the angle between the incident ray of light and the normal drawn to the surface at the point where the ray strikes.

Introduction / Context:
In geometrical optics, several angles are defined to describe how light interacts with surfaces such as plane mirrors, lenses, and transparent boundaries. One of the most fundamental is the angle of incidence, which appears in laws such as the law of reflection and Snell law of refraction. This question checks whether you remember the correct geometric definition of the angle of incidence.

Given Data / Assumptions:

• A ray of light (incident ray) strikes a surface, such as a mirror or glass boundary.
• A normal line is drawn at the point where the ray meets the surface. The normal is a line perpendicular to the surface at that point.

Concept / Approach:
By definition, the angle of incidence is the angle between the incident ray and the normal to the surface at the point of incidence. It is not measured with respect to the surface itself. Measuring with respect to the normal gives a consistent framework for both reflection and refraction, and is used in formulas such as Snell law (n1 sin i = n2 sin r), where i is the angle of incidence and r is the angle of refraction.

Step-by-Step Solution:
Step 1: Identify the incident ray, which is the ray of light approaching and striking the surface. Step 2: Draw the normal, which is a line perpendicular to the surface at the point of incidence. Step 3: Define the angle of incidence as the angle between the incident ray and this normal line. Step 4: Compare this definition with the given options and choose the one that mentions “normal to the surface and the incident ray”.

Verification / Alternative check:
The law of reflection states that the angle of incidence equals the angle of reflection, and both of these angles are measured with respect to the normal. Textbooks and standard diagrams always show the incident ray, reflected ray, and normal forming a plane, and the angles are marked between the rays and the normal. This consistent treatment confirms that the correct definition uses the normal, not the surface or tangent.

Why Other Options Are Wrong:

• Surface of the mirror and the incident ray: This would measure the angle from the surface, not from the normal, and is not the standard definition used in optics.
• Tangent to the surface and the incident ray: A tangent is parallel to the surface, so this option again effectively measures from the surface, not from the normal.
• Reflected ray and the incident ray: The angle between these two rays is sometimes of interest, but it is not called the angle of incidence. It is related but distinct.

Common Pitfalls:
Many learners mistakenly think angles are always measured from the surface because it feels more intuitive visually. However, using the normal simplifies the mathematical treatment of both reflection and refraction. Confusing the angle of incidence with the angle between incident and reflected rays can also cause errors when applying formulas. Always remember to draw the normal and measure angles from that line.

Final Answer:
The angle of incidence is the angle between the normal to the surface and the incident ray.