# Briefly describe how we could find the focal length of a concave mirror.

neela | High School Teacher | (Level 3) Valedictorian

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To determine the focal length of concave mirror.

We require a concave mirror preferably mounted on a stand, a lighted candle and a white screen to catch the image after reflection

Keep the mounted concave mirror on a plane surface (say a long table). Keep in front of the reflecting surface a bright candle at sufficient distance from the concave mirror  on the principal axis so that we can get a clear image somewhere. Now adjust the screen ,candle and the mounted concave mirror so that they are all on the principal axis. Move the screen back and forth and determine the position for the brightest clearest  image.

Note down for the clear image distance v and the corresponding object distance u from the pole of the mirror along the principal axis. Then, if f is the the focal length of the mirror, solve for f = uv/(u+v) which determines the focal length f on one single trial.

You make the following table of observation for repeated trials varying object distance u and the image distance v:

Trial no:  Dist u of object from the pole . Distance v of image from the pole. Focal legnth f = uv/((u+v)

After doing different trials you can find the average focal length from the last column.

revolution | College Teacher | (Level 1) Valedictorian

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To find the focal length of a concave mirror using a graphical method:

Apparatus:

1. converging lens
2. white screen
3. lens holder
4. torchlight
5. retort stand to hold torchlight

STEPS:

1. Place the apparatus on a long table. Adjust the appartus so that they all lie along the principal axis to get a clear image
2. Get an approximate reading of the focal length by focusing a distant object on the white screen. Record the value in a table
3. Next, set up the object and screen so the distance between them is around (9f/2)
4. Next, ensure that the lens' centre is the same height as the torch light
5. There would be about two positions that the lens could be placed that would be able to produce a sharp image on the white screen. Find the length of the 2 positions and record it.
6. Move the screen away from the object later in parts, like 3cm each time. For each value of the increased length, record until you have about six measurements of the extended length. Tabulate L, I, L^2, I^2 and (L^2-1^2).
7. Plot (L^2-I^2) against L, and find the gradient of the graph.
8. Given the equation of the experiment is (L2-I^2)=(4f)L, next equate the gradient to 4f, which the focal length can be found.

Adapted from one of the experiments that I taught in school using the graphical method.