To find the focal length of a convex lens by plotting a graph:
between μ and v between 1/μ and 1/v
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.
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.
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
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 |
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.
Scale; X’ axis: 1cm = 0.01 cm ^{-1} of 1/μ
Y’ axis: 1 cm = 0.01 cmcm ^{-1} of 1/v
From μ-v graph is, ƒ = 10.1 cm
From 1/μ-1/v graph is, ƒ = 10.2 cm
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