The reflection of light by spherical mirrors or curved surfaces, we will study in this topic. Before I explain the steps I would recommend you to learn basic fundamentals or terminology that we use for mirrors. 

1. Reflection of Light by Spherical Mirrors

Reflection of light from curved surfaces includes some basic terms that you need to understand. For this reason, I have listed the main points of this topic here, these are;

1. The angle of reflection
2. The angle of incidence
3. The incident ray
4. The reflected ray
5. The Normal and
6. The plane of mirror and light rays

If you are clear about these points which are basically the main concept of optics then you will not face any problem to visualize the picture of the reflection of light by any type of curved surface. To make it more clear, let me ask you some questions for the same;

What is the angle of reflection, how you will define it?

You will say, that the angle which develops between the reflected ray and the normal to the surface of the spherical mirror. And remember when you reply to any question you are aware of all the physical pictures of the concepts like you said here about the reflected ray and the normal to the surface. 

What is the angle of incidence, how you will define it?

The angle develops between the incident light ray and the normal to the surface of the spherical mirror. Remember, here we are using the word mirror.

What is the Incident Ray?

When the light from a distance source falls onto the plane, defined by the incident rays. In general, to explain the phenomena of “reflection of light” we consider only one light ray. The incoming light ray from a source to the plane is known as “incident light ray”.

Note: Further, you will study the light characteristics and its’ nature. Here, in this topic, you had used the geometrical symbol for the light in terms of an arrow. Next, for other explanations, you will see it in the form of a wave.  If you want to know more about it then you have to read the wave nature of light or Interference.

What is the Reflected Ray?

When the incident light strikes the curved surface at a point it gets reflected and one light ray from it is known as a reflected ray.  This light can be reflected in any direction, it depends on the incidence angle from the normal.

You are getting 100% light after reflection or not it depends on the characteristic of the spherical mirror.  

How you will define a Normal? 

A normal is a perpendicular line to the surface of a plane or point where light incident. When I am talking about the point in the earlier sentence, I am looking at the curved surface and the normal will be tangent to the surface.  

How do you see when you say that the Incident light, Normal, and the Reflected light are in the same plane? 

Now when you understand all the basic fundamental concepts of the incident ray, normal, and the reflected ray, the next point comes to think and visualize about to consider all 3 in a plane.

It is simple when you draw the reflection of light by any mirror on your notebook page you draw the incident line, normal, and the reflected light on that single page. You can consider a plane to this page.

I mean to say if the incident light you considered from the sun, a light bulb, or tube light the light will also reflect in the space. If you will draw a perpendicular to the incident point that will also be in the space. So, all these three will lie on the same plane.   

Again, when I am saying plane, I have a picture in my mind of a 3-dimensional space. That is have 3 planes perpendicular to each other like in a room or any other object. A plane along the X-axis, a second plane along the Y-axis, and a third plane along the Z-axis. 

In this picture No.2, I have created 3-planes to show you in favor of my statement mentioned above. So by this way, we can see that all these three incident rays, normal, and reflected rays lie in the same plane and it is plane 3 (SRKL).

I hope you get it without any doubt. If still there is any question you can ask it by using the comment box.

Now we will see some more concepts about spherical mirrors.  

Pole:

In general, we define it by the geometrical centre of the spherical mirror. If you are using a spherical lens then it is called an optical centre.

Principal Axis:

The principal axis is a line that joins the pole and centre of curvature. While in the spherical lens case, the principal axis joins the optical centre to the principal focus. 

Sign Convention in Spherical Mirrors

I hope this is very easy to understand, so no extra visualization is required. As you know all the distances are measured from the pole (in the case of a spherical mirror). If distances are in the same direction as of the incident ray then it will be positive otherwise it will be negative.

Similarly for the upward direction measurement will be positive and the downside measurement will be negative. The cartesian sign convention helps in these measurements.

In the next lecture notes, I will discuss some points about the concave mirror and convex mirror. 

Conclusion:

As you know the basic concepts about the law of reflection but when one asks how all the three incident rays, normal, and reflected rays lie in the same plane, that visualization becomes quite difficult. So in this lecture post, I have just covered this idea. I hope it will be useful.