The Periscope Designer's Challenge · AI Generator #GEN-7D05751F

Physics · optics

Problem

A submarine periscope designer needs to create a compact periscope system for a new vessel. The periscope uses two plane mirrors arranged at 45°45° angles to redirect the line of sight vertically. Due to space constraints, the horizontal separation between the two mirrors must be exactly d=30.0  cmd = 30.0\;\text{cm}. The designer wants the periscope to have a total height of H=2.40  mH = 2.40\;\text{m} from the bottom mirror to the top mirror. If light enters the top mirror horizontally and must exit the bottom mirror horizontally (both rays parallel to the ocean surface), what is the required vertical separation between the two 45°45° mirror positions?
Intuitive explanation

The key insight is that each 45°45° mirror rotates a light ray by 90°90°—so a horizontal ray becomes vertical after the first mirror, then horizontal again after the second. The vertical separation between mirrors determines how far the light travels vertically inside the periscope, while the horizontal separation dd constrains the geometry of the mirror placement. You need to use the geometry of the light path and the constraint that both mirrors are tilted at 45°45° to relate the vertical distance the light travels to the given horizontal separation and total height.

Intuitive explanation

The key insight is that each 45°45° mirror rotates a light ray by 90°90°—so a horizontal ray becomes vertical after the first mirror, then horizontal again after the second. The vertical separation between mirrors determines how far the light travels vertically inside the periscope, while the horizontal separation dd constrains the geometry of the mirror placement. You need to use the geometry of the light path and the constraint that both mirrors are tilted at 45°45° to relate the vertical distance the light travels to the given horizontal separation and total height.

Related theory

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