The Periscope Designer's Challenge · AI Generator #GEN-8DCE1E3E
Physics · optics
Problem
A submarine periscope designer needs to create a compact periscope that can view objects at the water surface while the submarine is submerged. The periscope consists of two plane mirrors arranged so that light from a surface object enters the top mirror, reflects to a bottom mirror, and then reflects to the observer's eye at the bottom of the periscope.
The periscope tube has a fixed length of L=4.0m and must fit within a cylindrical housing of diameter D=30cm. The designer wants to maximize the field of view angle θ (the maximum angle from the periscope axis at which surface objects can still be seen).
(a) If both mirrors are oriented at 45° to the periscope axis and have width w=12cm, what is the maximum field of view angle θ?
(b) The designer realizes they can improve the field of view by tilting the mirrors at different angles. If the top mirror is tilted at angle α to the periscope axis and the bottom mirror at angle β, what condition must be satisfied for light entering parallel to the axis to exit parallel to the axis?
(c) Using the condition from part (b), and keeping the mirror width at w=12cm, find the optimal angles α and β that maximize the field of view. What is the maximum field of view angle?