MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A laser pulse enters a long, narrow cavity whose walls reflect 80\% of the radiant energy incident upon them and absorb the rest. Each time the pulse strikes a wall, it is reflected back across the cavity; thus the pulse undergoes a sequence of reflections, losing energy every time it hits a wall. Assume the pulse makes its first contact with a wall carrying exactly 12 J of energy and that the geometry of the cavity forces the pulse to strike the walls alternately so that the sequence of energies lost at the walls continues indefinitely.
(a) Construct an expression for the total amount of energy ultimately absorbed by the walls. Clearly state any variables or constants you introduce.
(b) Evaluate the total absorbed energy in joules.
(c) After what number of wall impacts will at least 95\% of the total absorbed energy (found in part (b)) have already been absorbed? Show your reasoning.