# Concave mirror

A concave mirror is a type of spherical mirror whose reflecting surface curves inward, like a bowl. The focal length of a spherical mirror of radius of curvature $R$ is $f=R/2$.

## Find approx focal length of a concave mirror

The concave mirror converges rays parallel to its axis on the focus. The distance between the pole of the mirror and its focus is called focal length.

Let us find focal length of a concave mirror. Face the concave mirror towards the sun. Take a small piece of paper and fix it to the thin stick. Using the stick as a handle, hold the paper very close to the mirror. Now gradually take the paper away from the mirror, towards the sun. At all times hold the paper at a small angle to the mirror to allow sunlight to fall on the mirror.

After a certain distance you will see an oval spot on the paper. Adjust the position and the angle of the paper till you get a very small, almost round, bright spot. At this position measure the distance between the pole of the mirror and the paper. This distance is approximate focal length of the mirror. If you keep the paper there for some time, the paper will start burning because sunlight gets concentrated at one spot, producing a lot of heat.

## Nature of image formed by a concave mirror

Let us study the nature of the image formed by a concave mirror. First find the approximate focal length $$(f)$$ of a concave mirror. Then fix it vertically on a stand. Draw a long straight line on a table and place the mirror stand on it. The pole of the mirror should be exactly above the line. Now mark the point F and C on the line, at distances $$f$$ and $$2f$$ respectively from the mirror.

Make a small screen of stiff paper and fix it on another stand. The screen should be vertical, with its centre at the same height as the pole of the mirror. Place the screen stand on the line drawn on the table.

Light a candle and place it between F and C. The flame of the candle should be at about the same height as the pole of the mirror. Move the screen back and forth till you see an inverted image of the flame on the screen. What is the location of image and is it real, enlarged, and inverted. Keep the candle at different positions and try to get its image on the screen. What are the positions and characteristics of the image?

## Verification of mirror formula

The object distance $$u$$, image distance $$v$$, and the focal length $$f$$ of the mirror are related by,

\begin{align} \frac{1}{v}+\frac{1}{u}=\frac{1}{f}. \nonumber \end{align}

The pole of the mirror is taken as the origin and principal axis as the $$X$$-axis. Usually, the positive of the axis is taken along the incident rays. The distance between the pole and the object (candle) is $$u$$ and distance between the pole and the image (screen) is $$v$$. Note that both $$u$$ and $$v$$ are negative in present case.

You need a concave mirror, V-stand, screen, screen-stand, candle, matchbox, and a scale.

1. Firstly, find the approximate focal length $$(f)$$ of a concave mirror. Then fix it vertically on a V-stand. Draw a long straight line on a table and place the mirror stand on it. The pole of the mirror should be exactly above the line.
2. Light a candle and place it on one end of the line. The flame of the candle should be at the same height as the pole of the mirror.
3. Fix the screen on its stand. The screen should be vertical. Place the screen between the candle and mirror.
4. Analyse the nature of the image by moving the screen and/or mirror.
5. For three different values of $$u$$, find the value of $$v$$. Calculate $$f$$ by substituting in formula given above.

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