Class 12 Physics practical reading To find the value of v for different values of u in case of a concave mirror and to find its focal length.

Aim 

To find the value of v for different values of u in case of a concave mirror and to find its focal length.

Apparatus Required 

Optical bench, three uprights with provision for lateral movement, mirror holder, two pins, a knitting needle and a half metre scale.

Theory 

 The focal length 'f' of a concave mirror is related to the object distance u and image distance v by the mirror formula, given by 

           1/f = 1/u + 1/v

              f = uv/(u+v) 

The Cartesian sign conventions should be used for proper sign of u, v and f, according to which u and v as well as f are negative.

Ray diagram

Procedure 

1. Determine the approximate focal length of the concave mirror by getting a clear image of a distant object (say, a tree) on a wall or screen. Measure the distance between the mirror and the wall. 

2. Place the mirror upright near the one end of the optical bench and two other uprights having lateral movement. Ensure that the needles face the mirrors. 

3. Adjust the levelling screws provided in the optical bench to make the mirror vertical. Ensure that the principal axis of the mirror is parallel to the optical bench scale. 

4. Note the position of the index mark on the base of the mirror upright. Keep the object pin at a position so that its tip and pole of the mirror are on the same horizontal line and are separated by a distance equal to the length of the given knitting needle (say x cm). Record the position of the index mark of the object pin upright on the bench. Record the difference in positions of the mirror and object pin as y cm. The index corrections for the object distance u is (x - y) cm. This correction is algebraically added to the object distance. 

5. Repeat the step 4 to find the index correction for the image distance (between the mirror and the image pin). 

6. Keep the object pin at a distance of nearly 1.5 times the approximate focal length. Adjust the height of the needle 25 equal to the pole of the mirror. Keeping one eye closed and loking with the other, locate the clear image of the pin. It will appear to be enlarged. 

7. Keep the image needle at a distance of more than double the approximate length. Adjust its height so that the tip of the needle just coincides with that of the tip (inverted) of the image of the other needle. To differentiate between the two, insert a small priece of paper on the tip of one of the needles. Use side ways (lateral) motion screw to make the tips coincide. 

8. Move the eye sideways and see that there is no parallex between the image needle and the image of the object needle. If the need be, move the image needle forward or backward. When the parallax is removed, the tips will coincide and they will appear to be coinciding for all positions of the eye. 

9. Record the positions of the index marks of mirror, object pin and the image pin on the scale of the optical bench. 

10. Change the position of the object pin by a small distance (say, 2 cm) each time (away from the mirror) and readjust the image pin to remove the parallax. Record at least five different sets of observations.

Observations 

Precautions 

1. The pole of the mirror and the tips of the needles should be at the same height. 

2. The upright should be vertical. 

3. Parallax must be removed from tip to tip. 

4. Index correction should be applied. 5. The eye should be at least be 30 cm from the image needle. 

Sources of Errors

1. The needles are not at the same height. 

2. Index corrections not properly applied. 

3. Parallax not removed.