Question

A ray of light is incident at an angle \(30^{\circ}\) on a mirror, The angle between normal and reflected ray is (A) \(15^{\circ}\) (B) \(30^{\circ}\) (C) \(45^{\circ}\) (D) \(60^{\circ}\)

Short answer

The angle between the normal and the reflected ray is \(60^{\circ}\), corresponding to option (D).

Step-by-step solution

Write down the given information

We are given that the angle of incidence, which we will denote as \(i\), is \(30^{\circ}\). We are tasked with finding the angle between the normal and reflected ray.

Apply the law of reflection

According to the law of reflection, the angle of incidence is equal to the angle of reflection. This means that the angle of reflection, which we will denote as \(r\), is also \(30^{\circ}\).

Calculate the angle between the normal and reflected ray

Since we know that both the angle of incidence and the angle of reflection are \(30^{\circ}\) and the normal is perpendicular to the mirror, the angle between the normal and the reflected ray can be found by calculating the sum of the angle of incidence and the angle of reflection: \(30^{\circ} + 30^{\circ} = 60^{\circ}\) Therefore, the angle between the normal and the reflected ray is \(60^{\circ}\), which corresponds to option (D).

Key concepts

Angle of Incidence

The angle of incidence is a basic concept in the study of optics, specifically when we are dealing with reflection. Imagine a ray of light hitting a flat mirror. The angle of incidence is the angle between the incoming ray of light and the normal to the surface at the point where the light hits the mirror. The term "normal" here refers to an imaginary line that is perpendicular to the surface.

This angle is important because it directly determines the behavior of light upon hitting a reflective surface. When the incident ray, the normal to the surface, and the reflected ray are all drawn, they lie in the same plane. In the problem we are looking at, the angle of incidence is given as \(30^{\circ}\). That means the incoming light ray makes a \(30^{\circ}\) angle with the imaginary line that stands perpendicular to the mirror surface. This measure is vital in predicting the direction that the light will take after reflecting.

Angle of Reflection

The angle of reflection is a key aspect in understanding how light behaves when it reflects off a surface. According to the law of reflection, this angle is always equal to the angle of incidence. This means that if a light ray hits the mirror making a \(30^{\circ}\) angle with the normal line, it will bounce off at the same \(30^{\circ}\) angle on the other side of the normal.

This concept can be further illustrated by drawing it out: when the light hits the mirror, you can draw a line from the point of impact perpendicular to the surface, which represents the normal. The light ray coming in forms the angle of incidence with this normal, and the light ray reflecting away forms an equally large angle, which is the angle of reflection.

• Equal Angles: Angle of incidence \(=\) Angle of reflection
• Same Plane: Both angles lie in the same plane as the incident ray and normal

Normal to the Surface

The normal to the surface is an imaginary construct that plays a crucial role in understanding reflection. It’s defined as a line that is perpendicular to the surface where the light ray hits.

A vital property of the normal is that it serves as the reference point from which the angles of incidence and reflection are measured. Imagine standing on point "P" on a flat surface with light striking this point; if you point a stick straight upwards, forming a \(90^{\circ}\) angle with the surface, that stick would represent the normal.

A clear understanding of this concept is necessary because it establishes the geometric framework for analyzing incidents of light reflection. The consistency it provides is key in calculations because without it, quantitively measuring angles such as 30 or 60 degrees relative to the surface would be ambiguous.