Experiment to find the focal length of a concave lens using a concave mirror and a concave lens with the optical bench and needle method.
Apparatus
A concave lens, a concave mirror with a short focal length, three uprights, an optical bench, and a knitting needle.
Observations and Calculations
|
No. of obs. |
Position of | Observed | Corrected | f = p(-q) / p +(-q) | |||||
| Concave mirror M cm | Concave lens L cm | Needle at C cm | Needle at O cm | p = OL cm | q = CL cm | P cm | P cm | ||
| 1 2 3 |
|||||||||
Mean value of ‘f’=……..cm
Procedure
First, find the approximate focal length of the concave mirror. Direct it toward an open window and obtain a sharp image of a distant object on a white screen or paper. Measure the distance between the mirror and the screen. This distance gives the approximate focal length of the concave mirror.
Next, hold the mirror in front of a light source. Observe the sharp image formed on a wall or white paper when the rays converge at a single point — this shows image formation.
Then, determine the index correction between the lens and needle, and between the mirror and needle, using the knitting needle. Mount the concave mirror, concave lens, and parallax needles vertically on the optical bench.
Now, place the parallax needle in front of the concave mirror at a distance approximately twice the focal length of the mirror. Remove parallax by adjusting the needle’s position until the image is clear. This position represents the center of curvature (C) of the mirror.
After that, insert the concave lens between the mirror and its center of curvature without changing the mirror’s position. Remove the parallax again between the object needle and its inverted image formed inside the mirror. This new position of the needle, denoted as O, is further away from C.
Repeat the entire process three times, each time changing the lens’s position slightly. Record the positions of the lens (L), object needle (O), and the center of curvature (C). Measure OL = p and CL = q.
Apply the index correction to get accurate values of p and q. Since the image is virtual, take q as negative. Finally, calculate the focal length using the formula:
f=p(−q)p+(−q)f = \frac{p(-q)}{p + (-q)}
Precautions
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Use a concave mirror with a short focal length.
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Keep the mirror’s position fixed during the experiment.
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Remove parallax carefully to avoid observational errors.
Viva Voce
Q1. Why should the concave mirror have a short focal length?
Ans: It helps keep the mirror–lens combination convergent over a wider range.
Q2. Where will the image form if the object is placed at the center of curvature of a concave mirror?
Ans: The image will also form at the center of curvature.
Q3. What is the optical center of a lens?
Ans: It is a point inside the lens through which light rays pass without deviation in direction.