Interactive practical

Converging-lens focal length and magnification

Focus inverted images on an optical bench, read rulers and investigate focal length and magnification using two graphs.

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A-Level Physics

Converging-lens focal length and magnification

CCEA 1210 — matched to your course.

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Practical focus

Use real images to determine focal length and test the relationship between magnification and image/object distance.

Practical method

Aim

Determine the focal length of a converging lens and investigate magnification using \(\dfrac{1}{f}\) = \(\dfrac{1}{u}\) + \(\dfrac{1}{v}\).

Variables

Independent variable: object distance u
Dependent variable: image distance v (and image height)
Control variables: the same lens; the same illuminated object.

Apparatus

Converging lens in a holder
Illuminated object (cross-wire on a lamp box)
White screen
Metre rule
Ruler for image heights

Method

Estimate f by focusing a distant window onto the screen.
Place the object at a measured distance u greater than f and move the screen until the image is sharpest; measure v.
Repeat for at least five object distances, finding the sharp image from both directions and averaging.
Measure the object and image heights to find magnification.
Plot \(\dfrac{1}{v}\) against \(\dfrac{1}{u}\): a straight line with intercepts \(\dfrac{1}{f}\) on both axes.

Sample results

Lens f ≈ 0.15 m; object height 20 mm.

u / m	v / m	1/u / m⁻¹	1/v / m⁻¹	Magnification
0.200	0.600	5.00	1.67	3.0
0.250	0.375	4.00	2.67	1.5
0.300	0.300	3.33	3.33	1.0
0.400	0.240	2.50	4.17	0.60
0.600	0.200	1.67	5.00	0.33

Analysis

\(\dfrac{1}{u}\) + \(\dfrac{1}{v}\) = 6.67 m⁻¹ for every row, so f = 0.150 m. Magnification equals \(\dfrac{v}{u}\) (and image height/object height): 3.0 at u = 0.200 m, 1.0 at u = 2f = 0.300 m.

Uncertainty

Judging the sharpest image is uncertain by about ±5 mm. For v = 0.600 m this is <1%, but for v = 0.200 m it is 2.5%. The \(\dfrac{1}{v}\)–\(\dfrac{1}{u}\) graph averages these.

Errors and improvements

Problem	Effect	Improvement
Judging the sharpest image	v uncertain	Approach from both sides and average
Measuring to the lens holder edge	Systematic error in u and v	Measure to the optical centre
Object inside focal length	No real image	Keep u > f

Risk assessment

Hazard	Risk	Control measure
Hot lamp box	Burns	Allow to cool
Focusing sunlight	Eye damage or fire	Never point the lens at the Sun

Common mistakes

Using u and v measured from the holder rather than the lens centre.
Forgetting the image is inverted.
Using a diverging lens sign convention by mistake.

Worked analysis

u = 0.400 m, v = 0.240 m: \(\dfrac{1}{f}\) = \(\dfrac{1}{0.400}\) + \(\dfrac{1}{0.240}\) = 2.50 + 4.17 = 6.67 m⁻¹, so f = 0.150 m. Magnification = \(\dfrac{v}{u}\) = 0.60.

Common misconception

A distant object focuses at the focal point, but nearer objects form images further from the lens than f.

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