This experiment determines the focal length of a convex lens and a spherical mirror by studying image formation and verifying the mirror and lens equations using graphical methods.
What This Experiment Demonstrates
Image formation by lenses and mirrors
Verification of lens and mirror formulae
Determination of focal length using a graph
Apparatus Required
Convex lens
Concave mirror (or convex mirror if specified)
Optical bench with scale
Object needle or illuminated object
Screen
Meter scale
Theory
The relationship between object distance \( u \), image distance \( v \), and focal length \( f \) for lenses and mirrors is given by:
\[\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\]
Rearranging the equation:
\[\frac{1}{v} = -\frac{1}{u} + \frac{1}{f}\]
This represents a straight-line equation of the form \( y = mx + c \), where:
\( y = \frac{1}{v} \)
\( x = \frac{1}{u} \)
Slope \( m = -1 \)
Intercept \( c = \frac{1}{f} \)
Method (Convex Lens)
Place the convex lens on the optical bench.
Position the object needle at a known distance \( u \) from the lens.
Move the screen until a sharp image is formed.
Measure the image distance \( v \).
Repeat for different object distances.
Method (Spherical Mirror)
Place the mirror vertically on the optical bench.
Position the object needle in front of the mirror.
Adjust the screen to obtain a sharp image.
Measure object distance \( u \) and image distance \( v \).
Repeat for multiple object positions.
Observations
Record values of object distance and image distance.
Object distance \( u \)
Image distance \( v \)
Calculated values of \( \frac{1}{u} \) and \( \frac{1}{v} \)
Graph
Plot a graph of \( \frac{1}{v} \) (y-axis) against \( \frac{1}{u} \) (x-axis).
The graph should be a straight line with slope approximately equal to −1.
For guidance on plotting graphs and determining gradients accurately, visit our Graph Guide.
Calculations
From the graph:
\[\text{Intercept} = \frac{1}{f}\]
Hence, the focal length is:
\[ f = \frac{1}{\text{intercept}} \]
Result
The focal length of the given convex lens and spherical mirror is determined from the intercept of the graph, verifying the lens and mirror equations.
Sources of Error & Precautions
Ensure accurate alignment of object, lens/mirror, and screen.
Measure distances from the optical center of the lens or pole of the mirror.
Avoid parallax errors while reading the scale.
Ensure the image formed is sharp before taking readings.
Video Demonstration
Video courtesy of ATU Galway City (YouTube). Used for educational purposes under YouTube’s embedding policy.