# What is concave mirror

Spherical mirror: concave mirror and convex mirror

To talk about “Spherical Mirrors: Concave Mirrors and Convex Mirrors” we must first draw them:

Concave and arcuate mirrors where R is the radius of curvature, C is the center of curvature and V is the vertex (the **point of intersection between the reflecting surface and the optical axis). **

Let’s look at the features of the two mirrors in detail to see how to use them.

## concave mirror

A concave mirror is characterized in that it has the center of curvature C on the same side of the reflecting surface. Another definition that can be given is as follows:

**Is the radius of the sphere normal to the spherical surface at point P.**

### concave mirror

**Characteristics of the rays of a concave mirror**

**The incident rays (parallel to the optical axis) will converge (reflect) to a fixed point on the optical axis, called the focal point (the point where all the rays are focused)**

The distance between the focus F and the vertex V of the focus mirror of the concave mirror is called the focal length and is denoted by the letter f. For a spherical mirror of radius r:

**f = r / 2Incident rays passing through the fire will be reflected in parallel**

Concave mirror light In practice it is similar to the previous image but the arrows of the rays are reversed.

Incident rays passing through the center of curvature will be reflected in the same direction as the incident ray

Concave mirror – ray passing through the center

The rays that affect the vertex V are reflected rays symmetrical about the optical axis

Top Concave mirror Having defined the characteristics of the rays of a concave mirror, the image formation will be quite simple.

It is recommended to use a radius passing through the vertex and a radius passing through the center.

## Image formation in a concave mirror

**The image is produced by the following steps:**

From the object two light rays are drawn (in the example below we have chosen the tip of the pencil) so that they affect the mirror

(you can choose two of the four rays seen above)

- Two reflected rays are detected according to the signals given above
- The image is formed at the point of intersection of two reflected rays.
- In the following example we launch a beam passing through the focal point which will be reflected parallel to the focal axis and a beam passing through the center which will be reflected in the same direction as the incident ray:

Concave mirror Inverted pencil Two reflected rays intersect where our image is. Since the image is the intersection of the reflected rays, it is a real image.

We then obtain an image:

**RealReverseshriveledDepending on the position of the object in relation to the focus and center position, the image will have certain characteristics (see summary at the end of the article).**

## convex mirror

A convex mirror is characterized in that it has a center of curvature C on the opposite side of the reflecting surface. Another definition that can be given is as follows:

**The normal to a spherical surface is the extension of the radius of the sphere.**

**Convex mirror Characteristics of the rays of a convex mirror**

The incident rays will be reflected parallel (to the optical axis) so that the extension of the reflected rays will pass through a fixed point on the optical axis called the focal point (the point where all the rays are focused)

Radius of the convex mirror For a concave mirror, the distance from the focal point F to the vertex V of the mirror is called the focal length and is denoted by the letter f. For a spherical mirror of radius r:

f** = r / 2The rays whose extension passes through the focus will be reflected parallel toA convex mirror beam per focus is similar in practice to the previous one but the arrows of the rays are opposite.**

The incident ray whose extension passes through the center of curvature will be reflected in the same direction as the incident ray.

**convex mirror radius in the center**

The rays that affect the vertex V are reflected rays symmetrical about the optical axis

**Radius of the convex mirror for the vertex Having defined the characteristics of the radius of the convex mirror, the construction of the image will be quite simple.**

## Image formation in a convex mirror

**The image is formed in the same way as in a concave mirror:**

From the object two light rays are drawn (in the example below we have chosen the tip of the pencil) so that they affect the mirror (you can choose two of the four rays seen above)

**Two reflected rays are detected according to the signals given aboveThe image is formed at the point of intersection of the extension of the two reflected rays.**

In the following example we launch a ray whose extension will pass through the focal point which is parallel and parallel to the focal axis and a ray will be reflected

Take for the focal axis the extension of the reflected ray passing through the focal point;

In this case the image will be formed from the point of intersection of the extension of the reflected rays (drawn in red):

Convex mirror reflection is the extension of two reflected rays to intersect (meet) at the point where our image is located. Since the image is the intersection of the reflected rays, it is an imaginary image.

Then we get an image:

**virtual (as it is obtained by extension of rays)LawShrunken.Equation of Mirrors (or Equation of Conjugate Points)It is defined as:**

- Object distance o: The distance between the object and the top of the spherical mirror;
- Image distance i: the distance between the image and the vertex of the spherical mirror;
**Focal length f: The distance between the focal point and the top of the spherical mirror (f = r/2)**- The mirror equation The mirror equation tells us the relationship between quantities o, I and f:

1 / F = 1 / I + 1 / O

This relation is valid for concave and convex mirrors.

## Comments:

The three distances are written in alphabetical order to facilitate the memory task;

The image is real if it is obtained from the intersection of the reflected rays (it is formed in front of the mirror), it is virtual if it is obtained from the intersection of the extension of the reflected rays (it is formed behind the mirror) );

I and o are positive for real images and objects, negative for virtual ones;

f is positive for concave mirrors and negative for convex mirrors.

spherical mirror magnification

Magnification G is defined as the ratio:

G = – I / O

The image based on the value of G is:

**g < 0: backwards g > 0: right0**