To find the focal length of a convex lens by plotting graph between u and v | Class 12 | Physics Practical Copy | Handwritten with observations

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Aim: To find the focal length of a convex lens by plotting graph between u and v.

Important Terms(in which most students are confused):

Convex lens:
The lens which is thick at the center and thin at its edges.
Concave lens:
The lens which is thin at the center and thick at its edges. {Trick: Concave lens is the lens in whick a cave is formed at the center.}

01

Principal:

For an object placed at a distance u from the optical center of a thin convex lens of focal length f, a real

and inverted image is formed on the other side of the lens at a distance v from the optical center. The relation between these distances is:
1
f
 =
1
v
 -
1
u
[eq.1]
02

According to the new cartesian sign convention u is negative, but v is positive. Therefore, [eq.1] becomes,
1
f
 =
1
v
 -
1
(-u)

⟹
1
f
 =
1
v
 +
1
u

03

This equation shows that 1/v versus 1/u graph is a straight line of negative slope.
Graph of u versus v is a hyperbola. When u = v, then each equals 2f.

f =
uv
u + v

When an object is placed in front of a thin convex lens at a distance equals to 2f, a real and inverted image of same size as that of the object is formed at a distance equal to the distance of the object i.e., 2f on the other side of the lens.

04

If the object’s position lies in between distance 2f and distance f from the optical center of the lens then a real, inverted and magnified image is formed at a point beyond 2f from the optical center on the other side of the lens.

Thus, by measuring the distances u and v, the focal length of the convex lens can be determined using. The focal length of the lens may also be determined by plotting graphs between u and v.


05

Procedure:

  1. Obtain approx. value of the focal length of the convex lens by focusing the image of a distant object. It can be found by obtaining a sharp image of the Sun or a distant tree on a plane screen (so that the image can be seen clearly) placed on the other side of the lens and measuring the distance between the lens and the image with a scale. This distance will give a rough idea about the focal length, f of the convex lens used.
    06

  2. Place the optical bench on a horizontal platform, and using the spirit level, make it horizontal with the help of levelling screws present at the base of the bench.
  3. Fix the convex lens on an upright and mount it vertically near to the middle of the optical bench such that its principal axis is parallel to the optical bench. In this position, the lens would be perpendicular to the optical bench.
  4. To determine the index correction, bring a pin close to the lens. Adjust the index needle (a sharp-edged knitting needle can also be for this purpose) horizontally such that its one end touches one of the curved surfaces of the lens and the other end touches the tip of the pin. Note the positions of the uprights on the scale provided on the optical bench. The difference of the two would give the observed length of the index needle. The actual length between the tip of the pin and optical center O would be length of the index needle (as measured by a scale) plus half of the thickness of the lens because optical center of a double convex lens with surfaces of equal curvature is at its geometrical center. The difference of the two lengths gives the index correction. Find index corrections for both the pins.
    07

  5. Place the sharp pins on the left and right side of the lens respectively. Adjust the pins so that the heights of the tips of these pins become equal to the height of the optical center O of the lens from the base of the optical bench. Put a small piece of paper on one of the pins (say on the object pin) to differentiate it from the other pin (image pin).
  6. Displace the object pin to a distance slightly less than 2f from the optical center O of the lens. Locate the position of the real and inverted image on the other side of the lens above the image pin.
  7. Using the method of parallax, adjust the position of the image pin such that it coincides with the object pin.
  8. Note the upright position of the object pin, convex lens and image pin on the optical bench and record the readings.
    08

  9. Move the object pin closer to the optical center of the lens (2 cm or 3 cm).
  10. Repeat the experiment and record at least six sets of readings for various distances of object pin between f and 2f from the lens.

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