To find the focal length of a concave lens, using a convex lens | Class 12 | Physics Practical Copy | Handwritten with observations

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Aim: To find the focal length of a concave lens, using a convex lens.

Principal:

As we know that the image formed by a concave lens is always virtual and erect. Therefore, its focal length cannot be determined directly. However, it can be determined indirectly by introducing a convex lens in between the object and the concave lens and producing a real image.

01

A convex lens L1 converges the light rays starting from an object AB to form a real and inverted image at position I. If a concave lens(diverging lens) L2 is inserted between the lens L1 and point I1 then the image I behaves as the virtual object for the concave lens. A real and inverted image is formed at point I2 by the diverging lens (concave lens) L2. Thus, for the concave lens L2 the distance O2I will act as u
and O2I' will be v, respectively. It is important to note that the focal length of convex lens L1 must be smaller than the focal length of the concave lens L2. The second image I' is formed only when the distance between lens L2 and first image I is less than the focal length of L2.


02

Thus, we can calculate the focal length of the concave lens L2 by using the formula
1
f
 =
1
v
 -
1
u

f =
uv
u - v
[eq.1]

Here both distances u and v are positive for the concave lens.
Since u will be found to be less than v, f will always be negative.

03

Procedure:

  1. If the focal length of the given thin convex lens L1 is not known, then rough value of its focal length (f1) should be estimated first to ensure that its focal length is less than that of the concave lens.
  2. Place the optical bench on a rigid platform and using the spirit level, make it horizontal with the help of levelling screws present at the base of the bench.
  3. Place one upright mounted with pin at object O place, convex lens L1, and another the pin at the

    place of image I on the optical bench. We can put a small piece of paper on image pin to differentiate it from the image of object pin.
  4. Check the collinearity of the tip of image pin, optical centre O1 of convex lens L1, and the tip of image pin at I along a horizontal straight line which is parallel to the length of the optical bench. In this condition the planes of lens and both the pins would be perpendicular to the axis of the lens.
    04

  5. For the determination of the index correction, bring a mounted pin close to the concave lens L2. Adjust the index needle (a sharp-edged knitting needle would also serve the 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 two 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 centre O2 of the lens L2 would be length of the index needle (as measured by a scale) plus half of the thickness of the lens at its optical centre. The difference of the two lengths is the index correction.
    (The thickness at the center of the concave lens can be ignored if it is thin in size).
  6. Separate the object pin at O from the convex lens by a distance slightly greater than the focal length f1 of the lens.
  7. Locate its real and inverted image at point I on the other side of the lens by removing the parallax between the image at I and image of the object pin at O.
  8. Read the positions of the uprights holding the object at O, convex lens L1, and image pin at I and record these observations.

    05

  9. From now on, do not change the position of the convex lens L1 and the position of the object pin at O. Insert the concave lens L2 in between the convex lens L1 and image pin at I. Now the image of object pin will shift further from the convex lens L1 to a point I2Adjust the position of the concave lens so that the point I2 is sufficiently away from the point I1.
  10. In case the image formed by the combination of convex and concave lenses is not distinctly visible, try to see it on moving the concave lens nearer to the point I1 and to locate the image by using a pencil held in hand, and keeping the image pin at I1 as a guide to decide which way to shift the concave lens L2. After having seen the clear image at point I2 and ensured that it lies


    within the range of the optical bench, move image pin to locate the image (or point I2) more accurately using the method of parallax. Since the image forming at I2 is quite enlarged, it can be blurred.
  11. Note the position of uprights holding the concave lens and image pin, i.e., point I2 and the readings
  12. Change the position of upright holding the object pin at O and repeat the steps 6 to 11. Note the observations carefully.


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