A student was asked to measure the focal length of a converging lens - Leaving Cert Physics - Question 2 - 2009

1. Measure from the center of the lens: Always ensure that the measurement of image distance is taken from the center of the lens to avoid parallax errors.

2. Use a perpendicular measuring technique: The distance should be measured perpendicularly from the lens to the image to ensure accuracy. Avoid any angle that might distort the measured distance.

To determine the focal length (f) of the lens, we can use the lens formula:

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Where:

• For u = 20.0 cm, v = 65.2 cm: $\frac{1}{f} = \frac{1}{20} + \frac{1}{65.2} \approx 0.0515 \text{ cm}^{-1}$

• For u = 30.0 cm, v = 33.3 cm: $\frac{1}{f} = \frac{1}{30} + \frac{1}{33.3} \approx 0.0613 \text{ cm}^{-1}$

• For u = 40.0 cm, v = 25.1 cm: $\frac{1}{f} = \frac{1}{40} + \frac{1}{25.1} \approx 0.0641 \text{ cm}^{-1}$

Now calculate f for each set:

• For the first measurement (u=20, v=65.2): $f \approx 19.4 ext{ cm}$

• For the second measurement (u=30, v=33.3): $f \approx 16.34 ext{ cm}$

• For the third measurement (u=40, v=25.1): $f \approx 15.38 ext{ cm}$

Calculating the average focal length: $f_{average} = \frac{(19.4 + 16.34 + 15.38)}{3} \approx 17.04 ext{ cm}$

If the student placed the object 10 cm from the lens, a significant issue would arise: the image formed could be a virtual image. As the object distance approaches the focal length, the light rays diverge rather than converge to form a real image, making it challenging to locate the image on a screen. In addition, measurements taken at this distance may lead to inaccuracies due to the lack of a clearly defined image.