Focal length of a concave mirror – theory and experiment

Spherical mirror has two types – Concave mirror and Convex mirror. In this article, we are going to discuss the focal length of a concave mirror. Though, the focal length of both types of mirror has same definition and units, but the signs of focal length are different for these two mirrors. Here, we have included all these key points. Again, there is an experiment to determine the focal length of a concave mirror. The lab data and conclusion for this experiment are also discussed here.

Contents in this article:

  1. Focal length of a mirror.
  2. How to find the focal length of a mirror?
  3. Determining the focal length of a concave mirror experiment

Define focal length of a concave mirror

The focal length of a mirror is defined as the distance of its focal point from its pole. The focal length of a concave mirror is negative in sign if we consider the traditional sign convention rule for the mirror and lens. By the statement a concave mirror of focal length f we mean that the distance of the focal point of the mirror from its pole is f.

Focal length is the half of radius of curvature of the spherical mirror. If r be the radius of curvature of the mirror then its focal length will be {\color{Blue}f=\frac{r}{2}}.

Why is the focal length of a concave mirror negative?

A concave mirror produces a real image of any object, at the same side of the object from the mirror. According to usual sign convention rule, the position of the mirror should be considered as the origin and all distances at right side are positive and all distances at left side are negative. Again, the object is always placed at the left side and hence the concave mirror produces image at the left side i.e. negative side. Now, parallel ray coming from object at the left side will converge at a point at the left side or negative side, after reflecting from the mirror. This point is nothing but the focal point. Thus, the focal distance is negative for a concave mirror.

How to find the focal length of a concave mirror?

  1. There is an easy way to find the focal length of a mirror by observing the point at which every parallel rays coming from large distance meet. This point of meeting is the focal point. Now, measure the distance from the center of mirror (pole) to that point. This will give the focal length of the mirror.
  2. One can determine the focal length of the mirror more accurately by an experiment given at below.

Determining the focal length of concave mirror experiment with Lab report and conclusion

In this part, we are going to discuss the experiment for determining the focal length of a concave mirror with lab report and conclusion. The concept used is that the parallel rays coming from a large distance meet at a point which is the focal point of the mirror. Then the distance of that point from the mirror will be the focal length of the mirror.

Apparatus used

  • A concave mirror
  • Mirror stand
  • Mirror holder
  • A Screen
  • Screen holder
  • Measuring scale

Ray diagram

Ray diagram for determining the focal length of a concave mirror
Ray diagram for determining the focal length of a concave mirror

Procedure

  1. Place the concave mirror and the screen on a stand. The mirror and the screen should be facing each other.
  2. Choose an object whose image is to be formed on the screen be the mirror. The distance of the object should be long enough, ideally 50 cm from the mirror.
  3. Adjust the relative position of the mirror and screen to get a clear image of the object on the screen. It is better to fix the position of any of the mirror or screen and adjust the position of other.
  4. When you get the clear image of the chosen object, fix the screen and mirror at their respective positions. Then measure the distance between the mirror and the screen by a measuring scale. This distance will be the focal length of the mirror.
  5. Repeat this process for three or five times i.e. take three or five observations.
  6. The average value of the observations will be the final value of the focal length.

Experimental data (lab report)

SL. No.Position of concave mirror (x)Position of screen (y)Focal length = (y-x) cm
140 cm51 cm11 cm
240 cm51 cm11 cm
340 cm51 cm11 cm
Observation table

Claculation:

The average value of the focal length of the mirror is, {\color{Blue}f = \frac {11+11+11}{3}}

of, f = 11 cm.

Conclusion:

The focal length of the concave mirror is 11 cm.

A concave mirror has the focal length of 20 cm. Find its radius of curvature. If an object is placed at 30 cm from the mirror, then find the image distance.

The focal length, f = 20 cm. Then using the formula {\color{Blue}f=\frac{r}{2}} we get the radius of curvature of the concave mirror is, r = 2f

or, r = 40 cm. This is the radius of curvature of the mirror. (Answer).

Now, using the mirror formula for concave mirror we get, {\color{Blue} \frac {1}{f} = \frac {1}{v} + \frac {1}{u}}

Here, the object distance, u = 30 cm

Focal length, f = 20 cm

Then, from the above equation we get, the image distance is, v = 60 cm.

So, the image will form at a distance of 60 cm from the concave mirror. (Answer).

This is all from this article. If you have any doubt on this topic you can ask me in the comment section!

Thank you!

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