8 junio, 2024

Concave mirror: what it is, characteristics, examples, applications

What is a concave mirror?

He Concave mirror or convergent is a mirror with an almost always spherical shape, in which the reflecting surface is on the inner side of the sphere or rather on a part of it. Other curved shapes are also possible, such as the parabola.

With curved mirrors, such as the concave mirror, it is possible to achieve various images: enlarged, diminished or even inverted. Magnified images make it easier to see the fine details of an object.

In a concave mirror, magnification is achieved because the curvature allows light to be focused much like a lens does.

The mirror works as shown in the figure above. Incident horizontal light rays come from the left, where there is a distant source, such as the Sun. These rays obey the law of reflection, which states that the angle of incidence of the light ray is equal to its angle of reflection.

After being reflected, the rays intersect at a special point, point F or Focal point, because that is where the light is focused. By placing objects in different locations on the axis that passes through C, F and V, the various images are obtained.

For example, between the focal point and the vertex of the mirror is the ideal place to place the face when putting on makeup or shaving, because in this way an image with great detail is achieved that is not possible with a flat mirror.

Characteristics of a concave mirror

Before looking at how the image is formed, let’s carefully analyze the points and distances presented in this illustration:

-The center of the sphere to which the mirror belongs is at point C and R is its radius. Point C is known as center of curvature and R is the Radius of curvature.

The point V is the vertex of the mirror.

The line joining points C, F, and V is known as optical axis of the mirror and is perpendicular to its surface. An incident ray passing through these points is reflected in the same direction and in the opposite direction.

-The reflection of incident rays parallel to the optic axis intersect at point F, called Focal point of the mirror.

-Note that point F is approximately halfway between C and V.

-A the distance between F and V, denoted as Fit is called focal distance and is calculated as:

f = R/2

graphical method

As previously stated, depending on the point where the object is placed, various images are obtained, which are easily visualized through the graphic method for mirrors.

This method consists of drawing light rays coming from strategic points of the object and observing how they are reflected in the specular surface. The image is obtained by prolonging these reflections and looking where they intersect.

In this way, it is known if the image is larger or smaller, real or virtual -if it is formed behind the mirror- and upright or inverted.

Examples of concave mirrors

Let’s see some examples of images obtained by concave mirrors:

Object between F and V

By placing the object between points F and V we can obtain a magnified virtual image. To visualize it, three main rays are drawn, as shown in the lower illustration:

-Ray 1, which leaves the flame at point P, is parallel to the optical axis and is reflected passing through F.

-Ray 2: incident in such a way that it is reflected in a direction parallel to the optical axis.

-Finally, ray 3, which is radial, arrives perpendicular to the mirror and is reflected in the opposite direction, passing through C.

Note that the law of reflection is fulfilled in the same way as in the flat mirror, with the difference that the normal to the surface of the curved mirror changes continuously.

Actually, two rays are enough to locate the image. In this case, by prolonging the three rays, they all intersect at a point P’ behind the mirror, which is where the image is formed. This image is virtual -in reality it is not traversed by any luminous ray-, it is upright and it is also larger than the original.

Object between C and F

When the object is between the focal point and the center of curvature of the mirror, the image that is formed is real –it is not located behind the mirror, but in front of it-, it is magnified and inverted.

object beyond center

The illustration below shows the image formed by an object far from the center of the mirror. The image is formed in this case between the focal point F and the center of curvature c. It is a real image, inverted and smaller than the object itself.

Lateral magnification

We can ask ourselves how amplified or diminished is the image obtained by means of the concave mirror, for this we define the side magnificationdenoted as m. It is given by the quotient between the size of the image and the size of the object:

m = size of the image / size of the object

The image formed by a mirror can be less than the size of the object, even so, m is still called magnification or increase side.

concave mirror applications

The property of concave mirrors to magnify images is used in important applications ranging from personal grooming to obtaining energy. clean.

magnifying mirrors

They are commonly used in the boudoir for personal grooming purposes: applying make-up, shaving, and tying a tie.

reflecting optical telescope

The first reflecting telescope was created by Isaac Newton and makes use of a concave mirror plus a lens as an eyepiece. One of the mirrors of the Cassegrain-type telescope is concave and parabolic and is used to collect light at the focal point.

dental mirrors

Dentists also use concave mirrors to obtain a magnified image of the teeth, so they can examine the teeth and gums in as much detail as possible.

car headlights

In automobile headlights, the filament of the bulb is placed at the focal point of a concave mirror. The light rays originating in the filament are reflected in a bundle of parallel rays.

Often the mirror is spherical, but sometimes the parabolic shape is used, which has the advantage of reflecting in a parallel beam all the rays coming from the focal point and not just those near the optical axis.

solar concentrators

Light from a distant source such as the Sun can be focused on a point using the concave mirror. Thanks to this, the heat is concentrated at that point. On a large scale, with this heat a fluid can be heated, such as water or oil for example.

In this consists the concentrated solar power that tries to produce electrical energy by activating a turbine propelled by the concentrated heat of the Sun at one point. It is an alternative procedure to the semiconductor photovoltaic cell.

References

Giancoli, D. 2006. Physics: Principles with Applications. 6th. Ed Prentice Hall.
Giambattista, A. 2010. Physics. 2nd. Ed. McGraw Hill.
The Physics Classroom. Ray Diagrams for Concave Mirrors. Retrieved from: physicsclassroom.com.
Thomas, W. 2008. Conceptual Physics. McGraw Hill.
Tippens, P. 2011. Physics: Concepts and Applications. 7th Edition. McGraw Hill.

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