A student is determining the focal length of a converging lens by two methods.
First, he uses an auto-collimation apparatus with a plane mirror placed behind the lens.
He sets the distance D D\,D between the mirror and the illuminated object to 40.0 cm. He then moves the lens until a sharp image appears on a card next to the illuminated object. On a schematic diagram of this setup drawn to a scale of 1/10th1/10\text{th}1/10th (where 1 cm on the drawing represents 10 cm in reality), the measured distance f f\,f between the illuminated object and the lens is 1.5 cm.
Calculate the actual distance F F\,F between the illuminated object and the lens.
The student repeats the procedure for a distance D=60.0 cmD = 60.0\text{ cm}D=60.0 cm and obtains an actual distance of F=15.4 cmF = 15.4\text{ cm}F=15.4 cm. Calculate F1F_1F1, the average value of F F\,F from these two trials.
In a second method, the student removes the mirror and places a screen at a distance from the lens on the other side.
He measures the distance u u\,u between the illuminated object and the lens, and the distance v v\,v between the lens and the screen when a sharp image is formed on the screen. His readings are:
u=24.0 cm u = 24.0\text{ cm} u=24.0 cm v=42.0 cm v = 42.0\text{ cm} v=42.0 cmCalculate F2F_2F2, another value for the focal length of the lens, using the equation:
F2=uvu+v F_2 = \frac{uv}{u + v} F2=u+vuvAnother student suggests that F1 F_1\,F1 and F2 F_2\,F2 should be equal.
State whether your findings support this idea. Justify your statement by reference to the results.
Describe one precaution that should be taken in this experiment to obtain reliable results.
216 exam-style questions on CIE IGCSE Physics 3.2 Light, covering 3.2.1a Reflection of light, 3.2.1b Images in a plane mirror, 3.2.2 Refraction of light, 3.2.2a Refraction of light, 3.2.2b Total internal reflection, 3.2.2c Refractive index and critical angle, 3.2.2d Optical fibres, 3.2.3a Converging and diverging lenses, 3.2.3b Ray diagrams and the nature of images, 3.2.3c Virtual images and the magnifying glass, 3.2.3d Correcting long-sightedness and short-sightedness, and 3.2.4 Dispersion of light. Each one has a worked solution and a mark scheme showing where the marks go.