How to Determine Focal Length of Concave and Convex Mirrors

A curved mirror in which a reflective surface bulges out towards the light source is known as a convex mirror. The convex mirror reflects the light outwards and so it is not used to focus light. As the object comes nearer to the mirror, the size of the object gets larger until it reaches its original size. These mirrors are also known as diverging mirrors.

A concave mirror has a reflecting surface that caves inwards. The mirror also converges the light at one prime focus point; hence they are also called converging mirrors. They are applied to focus light. Depending upon the location of the object with respect to the mirror, the size of the image formed by the concave mirror varies. It can be real or virtual, inverted or erect and magnified, reduced, or be similar in size of the object depending upon the position.

Focal Length of Concave Mirror

This article will help you find the focal length of a concave mirror. Let’s look at the theory to obtain the image of a farther object.

1. Like a plane mirror, the concave mirror obeys the law of reflection of light.

2. Ray of light from an object – The rays of light emitted from a distant object, e.g., distant buildings or sun, are parallel to each other. When the parallel rays from the source fall on the concave mirror along the axis, reflect and meet at the point in front of the mirror, which is known as the mirror's principal focus.

3. At the focus of the mirror, a real, inverted, and very small image size is formed. 

4. Focal length – Focal length of the concave mirror is the distance between the pole P of the concave mirror and the focus F. By obtaining the Real image of the distant object, the focal length of a concave mirror can be determined, as shown in the di

Focal Length of Concave Mirror Formula

Let’s see the above-shown diagram, 

Focal Length – The space between the pole P of a concave mirror and the focus F is the focal length of a concave mirror. By obtaining the Real image of a distant object at its focus, the focal length of the concave mirror can be estimated as shown in the diagram.

The focal length of the convex mirror is positive, whereas that of the concave mirror is negative. The same can also be proved by using the mirror formula:

\[\frac{1}{f}\]=\[\frac{1}{v}\]-\[\frac{1}{u}\]

Let's see how

Since we know that an object is always placed at the left side or direction opposite the incidence ray of the mirror, the object distance will always be negative.

u = -u

v = -v (Image distance is negative since images produced by concave mirrors are usually on the left side or direction opposite to the incidence ray)

Using mirror formula,

 \[\frac{1}{f}\]=\[\frac{1}{v}\]-\[\frac{1}{u}\]

Or \[\frac{1}{f}\]=\[\frac{u-v}{uv}\]

Or \[f=\frac{uv}{u-v}\]

Focal Length of Convex Mirror Using Convex Lens

A curved mirror in which the mirroring surface bulges towards the light source is known as the convex mirror. The light is reflected outwards in a convex mirror; therefore, they are not used to focus light. The convex mirror is also called a diverging mirror or fish-eye mirror.

The image created by a convex lens is erect and virtual since the focal point (F), and center of curvature (2F) are both imaginary points within the mirror that cannot be reached. As a result, the image formed by these mirrors cannot be projected on the screen as the image is inside the mirror. Hence the focal length cannot be determined directly. Initially, the size of the image is smaller than the object, but it gets larger as the object approaches the mirror. The diagram below shows the convex mirror.

(the image will be uploaded soon)

The focal length of a convex mirror can be determined by introducing the convex lens between the object and the convex mirror. With the help of a convex lens side by side with an object, an image can be obtained when the convex mirror reflects the rays along the same path, i.e. when rays fall naturally on the mirror. The space between the screen and the mirror is the radius of curvature, which is denoted by R.

By using the formula below, the focal length f of the convex mirror can be calculated.

\[F=\frac{R}{2}\]

Where,

R-Radius of curvature

A mirror with a reflecting surface facing outwards is a Convex mirror, whereas a mirror with a reflecting surface facing inwards is a Concave mirror. The coating of the Convex mirror is on the outside of the spherical surface while the coating of the Concave mirror is on the inside. 

For a Convex Mirror, the principal focus is behind, whereas, for a Concave Mirror, the principal focus is at the front. A point at which the reflected rays meet or appear to meet is the Principal focus.

To find the focal length of a Concave mirror:

The various ways to obtain the focal length of the concave mirror:

i)A spherical mirror whose reflecting surface is curved inwards and follows laws of reflection of light is a Concave mirror.

ii) The light rays that come in from a distant object are considered to be parallel to each other.

iii) The parallel rays of light will meet the point in the front of the mirror if the image formed is real, inverted, and small in size.

(Image will be uploaded soon)

iv) The image formed by the convex lens is real and can be obtained on the screen.

v)  the symbol ‘f’ is used to denote the difference between the principal axis P and the focus F of the concave mirror.  

To find the focal length of a Convex mirror:

The various ways to obtain the focal length of the convex lens:

• The middle part of the convex lens is thicker and the edges are thinner.  This is known as a converging lens.

• The refracted rays from the parallel beam of light converge on the other side of the convex lens.

(Image will be uploaded soon)

• The image would be real if the image is obtained at the focus of the lens,  inverted and very small.

• ‘f’ is the focal length which is the difference between the optical center of the lens and the principal focus.

• As the image formed by the lens is real, the image can be obtained on the screen.

(Image will be uploaded soon)

The procedure of determining the focal point of a Concave Mirror can be explained as follows: 

• The distance between the selected object should be more than 50 ft.

• The concave mirror placed on the mirror stand and the distant object should be facing each other.

• The screen should be in front of the reflecting surface of the mirror and to be able to get a sharp image, adjustments should be made to the screen.

• The distance between the concave mirror and screen can be determined by using a meter scale. The distance and focal length of the mirror will be the same as the given Concave Mirror.

• To calculate the average focal length, we will have to repeat the above procedure three times.

The procedure of determining the focal point of a Convex Lens can be explained as follows: 

• Arrange both the lens and the screen of them on the wooden bench.

• The lens should be placed on the holder in such a way that it is facing a distant object.

• Holder should be placed with the screen on the bench.

• The position of the screen should be such that the sharp image of the distant object is obtained on it.

• The difference between the two positions i.e. of the lens and of the screen has to be equal to the focal length of the given convex lens.

• Shift the focus towards various other distant objects in order to calculate the focal length of the convex lens.