A theatrical lighting designer mounts a concave spherical mirror with a radius of curvature of 1.20 m at the back of the stage. A vertical test object 45 cm tall is placed on the principal axis 80 cm in front of the mirror.
Using only the information above, construct and analyse a scale ray diagram to investigate the image formed by the mirror.
(a) On your answer sheet, draw the principal axis, sketch the mirror with its vertex at the origin, and mark the focal point at the correct scaled location. Using a convenient linear scale (for example, 1 cm on paper represents 10 cm in reality), draw the object and the three principal rays needed to locate the image.
(b) From your diagram, measure the image distance si and image height hi. State your measured values with appropriate units and the scale factor used.
(c) Using appropriate quantitative relationships for spherical mirrors, calculate the theoretical image distance and lateral magnification for this object–mirror arrangement. Show all mathematical steps and include units in your final answers.
(d) Compare the values obtained in parts (b) and (c). Discuss at least two possible reasons for any discrepancy between the diagram-based measurements and the calculated results.