The Periscope Fish Tank · AI Generator #GEN-CE684D3F

Physics · optics

Problem

A marine biologist wants to observe fish behavior from above using a periscope-like device. The device consists of two parallel plane mirrors separated by a distance d=40  cmd = 40\;\text{cm}, with the upper mirror at a 45°45° angle to the horizontal and the lower mirror also at 45°45° but oriented to redirect light upward. The fish tank has a glass bottom with thickness t=8  mmt = 8\;\text{mm} and refractive index nglass=1.50n_{\text{glass}} = 1.50. Below this glass bottom is an air gap of height h=12  cmh = 12\;\text{cm}, and then the lower mirror. A fish swimming at depth D=25  cmD = 25\;\text{cm} below the water surface appears to be at a certain apparent depth when viewed through this periscope system. The refractive index of water is nwater=1.33n_{\text{water}} = 1.33. (a) What is the apparent depth of the fish as seen by an observer looking down through the periscope? (b) If the fish moves horizontally by a distance x=15  cmx = 15\;\text{cm} from its original position, by what horizontal distance does its image appear to shift as viewed through the periscope?

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