Problem 1 - College Physics

Question

The angle of incidence of a light ray on a mirrored surface is \(30^{\circ} .\) What is the angle between the incident and reflected rays?

Step-by-Step Solution

Answer

The angle between the incident and reflected rays is \(60^{\circ}\).

Step 1: Understand Angle of Incidence

The angle of incidence is the angle formed between the incoming light ray and the normal (a line perpendicular to the surface at the point of incidence). For this problem, it is given as \(30^{\circ}\).

Step 2: Apply Law of Reflection

According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, the angle at which the light ray reflects off the surface also measures \(30^{\circ}\).

Step 3: Find the Total Angle Between the Rays

The angle between the incident ray and the reflected ray can be found by adding the angle of incidence and the angle of reflection together. Thus, the total angle is \(30^{\circ} + 30^{\circ} = 60^{\circ}\).

Key Concepts

Law of Reflection

The Law of Reflection is a fundamental principle in physics, especially when studying light and optics. It states that the angle of incidence is always equal to the angle of reflection. This means that when a light ray hits a surface, the angle at which it arrives (incidence) is the same as the angle at which it departs (reflection).

To visualize this, imagine a light ray striking a smooth surface such as a mirror. At the point of contact, you can draw a line called the "normal" that is perpendicular to the surface. The angle of incidence is formed between the incoming ray and the normal. According to the law of reflection:

• The angle of incidence = angle of reflection
• Both angles are measured with respect to the normal
• This law applies to smooth, reflective surfaces

Knowing this law helps in predicting the path of light rays and understanding phenomena such as how mirrors work.

Angle of Reflection

The angle of reflection is an essential term when dealing with mirrored surfaces and light behavior. As per the law of reflection, this angle is equal to the angle of incidence.

If you have a light ray that makes a certain angle with the normal, called the angle of incidence, the angle of reflection will be the same measurement away from the normal on the opposite side. Imagine standing in front of a mirror. Light bounces off your face and hits the mirror at a certain angle. This light then reflects off the mirror at an equal angle. This is the very same angle of reflection that guides much of our understanding of light in everyday mirrors.

In the exercise, the angle of incidence was given as \(30^{\circ}\). By the law of reflection, the angle of reflection is also \(30^{\circ}\). When these two rays—the incident and the reflected—form an angle together, it proves the consistency and reliability of the angle of reflection as a measurable and predictable aspect of reflected light.

Mirrored Surface

A mirrored surface is a type of surface that reflects light following the law of reflection. When light encounters such a surface, the angle at which it hits the surface determines how it will reflect.

Mirrors are smooth surfaces that have been polished or coated with a reflecting material, such as silver. This coating ensures that almost all incoming light is reflected, rather than absorbed or scattered.

• The smoothness of the surface plays a crucial role in determining the quality and accuracy of the reflection.
• Any irregularities or roughness can scatter light in multiple directions, which is known as diffuse reflection.
• Each ray of light that strikes a mirrored surface reflects predictably by forming equal angles with the normal.

Mirrored surfaces are used in a wide variety of applications, from making telescopes and cameras to everyday items like bathroom mirrors, because they enable clear, undistorted reflection of light.