A student performs an experiment to determine the focal length fff of a thin converging lens. They measure various object distances uuu and the corresponding image distances vvv, and plot a graph of v / cmv\text{ / cm}v / cm on the yyy-axis against u / cmu\text{ / cm}u / cm on the xxx-axis.
The student draws a straight line on the graph connecting the coordinates (25.0,25.0) cm(25.0, 25.0)\text{ cm}(25.0,25.0) cm and (45.0,45.0) cm(45.0, 45.0)\text{ cm}(45.0,45.0) cm. State the equation of this line.
The straight line intersects the experimental curved graph at the point where u1=34.8 cmu_1 = 34.8\text{ cm}u1=34.8 cm and v1=34.8 cmv_1 = 34.8\text{ cm}v1=34.8 cm. Calculate the focal length fff of the lens using the equation:
f=u1+v14 f = \frac{u_1 + v_1}{4} f=4u1+v1By substituting u=vu = vu=v into the thin lens formula:
1f=1u+1v \frac{1}{f} = \frac{1}{u} + \frac{1}{v} f1=u1+v1show that the equation f=u1+v14f = \frac{u_1 + v_1}{4}f=4u1+v1 is mathematically correct for the intersection point where u1=v1u_1 = v_1u1=v1.
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.