A student is investigating the refraction and reflection of light in a transparent rectangular block. The theory suggests that a certain angle θ \theta\,θ and the angle of incidence i i\,i are related by the formula: θ=2i\theta = 2iθ=2i.
In the first run of the experiment, the angle of incidence is set to i=35∘i = 35^\circi=35∘. The student measures the angle θ \theta\,θ to be 71∘71^\circ71∘. (i) Calculate the value of 2i 2i\,2i for this run.
(ii) Calculate the difference (θ−2i)(\theta - 2i)(θ−2i) for this run.
In the second run of the experiment, the student uses an angle of incidence i=45∘i = 45^\circi=45∘ and obtains a measured value of θ=88∘\theta = 88^\circθ=88∘. Calculate the difference (θ−2i)(\theta - 2i)(θ−2i) for this run.
State whether the results from parts (a) and (b) support the theory that θ=2i\theta = 2iθ=2i. Justify your answer by referring to your calculated differences.
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.