An engineer is designing a simple periscope that allows a submarine crew member to…
PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction
Problem
An engineer is designing a simple periscope that allows a submarine crew member to observe aircraft flying overhead. The periscope consists of two identical plane mirrors separated by a vertical distance of 2.0 m inside a long tube. Each mirror can be tilted about a horizontal axis but is otherwise fixed in position. The observer’s eye is level with the lower mirror.
An aircraft approaches such that the line of sight from the top mirror to the aircraft makes a 25∘ angle above the horizontal.
(a) Determine the angle each mirror must make with respect to the vertical in order for the observer to see the aircraft. State clearly the orientation of both the top and the bottom mirror.
(b) The aircraft climbs so that the line of sight to it from the top mirror is now 40∘ above the horizontal, while the submarine remains at the same depth. If only the top mirror is adjusted, by how many degrees must it be rotated so that the observer can still see the aircraft? Justify your answer quantitatively.
(c) Discuss one practical limitation that would arise if the periscope used mirrors that could rotate only within ±45∘ of the vertical. Relate your discussion to the results obtained in parts (a) and (b).