Question

± PSS 34.1 Image Formation by Mirrors

Learning Goal:

To practice Problem-Solving Strategy 34.1 Image Formation by Mirrors.

(Figure 1) Consider an object located at position P in front of a concave mirror whose center of curvature is at position C, as shown in the diagram. Draw a principal-ray diagram to determine the size and position of the reflected image.

This problem involves using graphical methods to find the image produced by the mirror. Writing down equations will be of no use here because you are not given any quantitative information about the mirror or the object. Instead, you can draw a principal-ray diagram.

Based on the information available in the problem introduction, which of the following principal rays can you draw to locate the image reflected by the mirror?

Check all that apply.

Check all that apply.

	a ray along the radius through the center of curvature C of the mirror
	a ray through (or proceeding toward) the focal point of the mirror
	a ray to the vertex V of the mirror
	a ray parallel to the optic axis of the mirror

Answer 1

Concepts and reason

The concept required to solve this problem is rules of forming ray diagram through concave mirror.

In this problem first identify the given points through which rays cannot pass, then identify the points through which rays can pass to make a complete diagram of the image. Finally, draws the ray diagram to represent the position and size of the image diagrammatically.

Fundamentals

Rules for ray diagram for concave mirrors are written as follows:

1.Any incident ray passing through the focal point of the mirror show get reflected parallel to the principle axis.

2.Any incident ray travelling parallel to the principle axis show get reflected and pass through the focal point of the mirror.

3.Any ray passing thorough the center of curvature of the of the mirror should get reflected and pass through the same line.

The figure given in the question is drawn below.

In the figure three points on the principle axis has been marked, P, C and V. P is the point where object is located, C is the center of curvature of the mirror, and V is the center of aperture of the mirror.

In this figure focal point is not marked, hence we can not draw any line passing thorough that point.

Second statement says that the ray passing through the focal point can help in the formation of image. This is true according to the rules but in the figure 1 focal point is not marked hence, this statement will not help in the formation of ray diagram of the image formation.

Fourth statement says that the ray parallel to the principle axis can help in the formation of image. This is true according the rules, but as we know that a parallel ray to the principle axis passes through the focal point after reflection. As the focal point is not marked hence, this statement will not help in the formation of ray diagram of the image formation.

First statement says that a ray passing through the center of curvature can help in the image formation which is true. We can apply rule number three given in the fundamental section. Hence, this is one of the correct statements which can help in the formation of ray diagram of image.

Third statement says that a ray to the vertex that is the center of aperture of the mirror can help in formation of the ray diagram. Vertex is given in the diagram and is represented as V. Hence, this is one of the correct statements which can help in the formation of ray diagram of the image.

Using first and third statement the ray diagram of the image formation is as follows:

Ans:

A ray along the radius and passing through the center of curvature.

Answer 2

Here is the whole problem (all the parts) worked out!! https://youtu.be/ovc6iQBEmV0