Class 12 Physics Lab Experiments

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

May 28 2023

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.

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:

μ-v graph:

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.

1/μ-1/v graph: The graph is a straight line

Scale; X’ axis: 1cm = 0.01 cm ^-1 of 1/μ

Y’ axis: 1 cm = 0.01 cmcm ^-1 of 1/v

Result:

From μ-v graph is, ƒ = 10.1 cm

From 1/μ-1/v graph is, ƒ = 10.2 cm

Precautions:

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