The Periscope with a Twist · AI Generator #GEN-A0D08444
Physics · optics
Problem
A submarine periscope uses two parallel mirrors inclined at 45° to the horizontal to allow viewing of the surface from below water. An engineer modifies the design by replacing the bottom mirror with a thin converging lens of focal length f=15.0cm, while keeping the top mirror in the same position. The distance between the lens and mirror along the light path is d=60.0cm.
A ship on the surface appears to subtend an angular size of θ=2.0° when viewed directly. When viewed through this modified periscope, the ship's image appears at the same location as it would in the original periscope (at the mirror surface), but now subtended a different angular size.
Find the angular magnification of this modified periscope system, defined as the ratio of the angular size seen through the periscope to the angular size seen directly.