A large aquarium has portholes of thin transparent plastic with a radius of curv

Question

A large aquarium has portholes of thin transparent plastic with a radius of curvature of 1.65 m and their convex sides facing into the water. A shark hovers in front of a porthole, sizing up the dinner prospects outside the tank.

A) If one of the shark’s teeth is exactly 47.5 cm from the plastic, how far from the plastic does it appear to be to observers outside the tank? (You can ignore refraction due to the plastic.)

B) If the tooth has an actual length of 5.00 cm, how long does it appear to the observers?

Explanation / Answer

here,

focal length = radius of curvature/2
f = 1.65/2
f = 0.825 m
object distance, d = 47.5 cm = 0.475 m

Part A :
From thin lens formula,
1/f = 1/d + 1/i

solving for image distance, i

1/di = 1/f - 1/do
di = (f*do) / (f-do)
di = (0.825*0.475) / (0.825 - 0.475)
di = 1.12 m

Part B:

Image height / Object height = Image distance / Object distance
hi/ho = di/do
hi/0.05 = 1.12/0.475
hi = 0.117 m

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