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Home Physics Class 12 Physics To find the focal length of a convex lens by plotting a graph
Class 12 Physics Lab Experiments

To find the focal length of a convex lens by plotting a graph



Aim

To find the focal length of a convex lens by plotting a graph:

between μ and v between 1/μ and 1/v

Apparatus

An optical bench with four uprights (2 fixed upright in middle two outer uprights with lateral movement), convex lens, convex mirror, a lens holder, a mirror holder, 2 optical needles (one thin, one thick), a knitting needle, a half meter scale.

Ray Diagram

Formulae Used:

The relation between ƒ, v and f for convex lens is: 1/ƒ = 1/v + 1/μ

Where, ƒ = Focal length of length of convex lens

μ= Distance of object needle from lens’ optical centre.

v = Distance of image needle from lens’ optical centre.

Observation:

Rough focal length of of the Lens = 10cm

Actual length of knitting needle, x = 15 cm.

Observed distance between object needle & the lens when knitting needle is placed between them, y = 15.2 cm.

Observed distance between image needle & the lens when knitting needle is placed between them, z = 14.1 cm.

Index correction for the object distance μ, x – y = – 0.2 cm

Index correction for the image distance v, x – z = +0.9 cm

Observation Table:

S.No. Position of:cm/Object needle/Lens/Image Needle μ(cm) v(cm) 1/v (cm-1) 1/μ (cm-1)
1 66 50 26 16 24 0.041 0.062
2 67 50 27 17 23
3 68 50 28 18 22 0.045 0.055
4 70 50 30 20 20 0.05 0.05
5 75 50 33 23 17 0.058 0.043
6 80 50 34 24 16 0.062 0.041

Calculations:

  1. μ-v graph:
  2. The graph is a rectangular hyperbola: Scale: X’ axis: 1 cm = 5 cm of μ Y’ axis: 1 cm = 5 cm of v

    AB = AC = 2 ƒ or OC = OB = 2ƒ

    ∴ ƒ = OB/2 and also ƒ = OC/2

    ∴ Mean value of ƒ = = 10.1 cm.

  3. 1/μ-1/v graph: The graph is a straight line
  4. Scale; X’ axis: 1cm = 0.01 cm -1 of 1/μ

    Y’ axis: 1 cm = 0.01 cmcm -1 of 1/v

    Iu vs Iv Curve

    Result:

    From μ-v graph is, ƒ = 10.1 cm

    From 1/μ-1/v graph is, ƒ = 10.2 cm

    Precautions:

    1. Tips of object & image needles should be at the same height as the centre of the lens.
    2. Parallax should be removed from tip-to-tip by keeping eye at a distance at least 30 cm. away from the needle.
    3. The image & the object needles should not be interchanged for different sets of observations.