Experiment: To Determine the Focal Length of a Convex lens by Plotting Graphs Between u and v and 1/u and 1/v

Mai 14, 2025

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par

Rajansmoorthy

dans PHYSICS, NEET, JEE, EDUCATION

Focal length of a convex lens: Objective

To find the focal length of a convex lens using the lens formula by plotting

u and v graph

1/u and 1/v graph

Focal length of a convex lens: Apparatus and Material Required

Convex lens (let’s assume f=10 cm)

Optical bench with 3 uprights (with clamps)

Optic needles

Meter scale

Spirit level 

Focal length of a convex lens: Ray Diagram

Focal length of a convex lens: Formula

Focal length of a convex lens: Theory

The lens formula is given by

1/v -1/u =1/f

Where

u= Object distance (always taken as negative in sign convention)

v= image distance

F+ focal length of the given lens (positive for convex lens)

Focal length of a convex lens: Procedure

Approximate focal length of the  convex lens by Distant object method

Prior to beginning the experiment, use the distant object method to determine the approximate focal length of the given convex lens (obtaining the sharp image of a distant tree on a plane wall or screen).

By calculating the distance between the lens and the image, you may get the approximate focal length.Take it as « f, » and you can note the matching.

Adjust the height of the convex lens by placing it on the optical bench almost in the center.

On either side of the convex, position the two needle-equipped uprights.

The needle pins P and P’ should be adjusted such that their tip heights match the height of the optical center O.

Obtain seven distinct readings for various u values.

A single measurement at (u = 2f) (20 cm)

Three measurements for u < 2f [14, 16, and 18 cm, for example]

For u ＞ 2f, three measurements [e.g., 22 cm, 24 cm, 26 cm]

Adjust the image pin P’s position using the parallax method such that the image of pin P and image pin P’ coincide.

Find the locations of the inverted and genuine images above image pin P’ on the other side of the lens.

A table should contain u and v.

Determine 1/u and 1/v for every measurement.

Plot two graphs:

Graph 1: u (on the X’-axis) versus v( on the Y-axis)

1/v (Y-axis) versus 1/u (X’-axis) in Graph 2

Using the graphs, get the focal length of the specified convex lens. 

Focal length of a convex lens:Observations and calculations (Assuming f = 10 cm)

Focal length of a convex lens: Tabular column for graphical determination

Focal length of a convex lens: Graphs

u vs v Graph:

X’- axis: u [Object distance (in cm)]

Y – axis: v [Image distance (in cm)]

The graph will be a hyperbolic curve

The point where (u=v=20 cm) gives 2f

The focal length of the lens f = OA/2  =OB/2=20/2 =10 cm

1/u vs 1/v graph:

X’- axis: 1/u [Object distance (in cm^-1)]

Y – axis: 1/v [Image distance (in cm^-1)]

The graph will be a straight line

The X’- intercept and Y-intercept  both give 1/f

From the graph:

X’-intercept = 1/f =1/0.1= 10 cm

Y- intercept = 1/f =1/0.1= 10 cm

Focal length of a convex lens: Result

The focal length of the given lens is determined to be

By experimental method      =10 cm

By u-v graphical method      =10 cm

By  1/u-1/v  graphical method = 10 cm

Focal length of a convex lens: Precautions

Make that the needles and lens are in line(aligned)

Accurately measure the object and image distances. 

For accurate image position, use the parallax approach.

For precise readings, take clear, sharp picture formations. 

Links to this post

Class 11 Physics Practicals: Hands-on Experiments to Master Key Concepts