How Does a Diving Mask Alter the Perceived Distance of Objects Underwater?

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SUMMARY

The discussion focuses on the optical effects of a diving mask with a convex spherical surface on the perceived distance of objects underwater. The specific scenario involves a diving mask with a radius of curvature of 0.50 m and a fish located 2.5 m away. Using the lens maker's equation, participants calculated the apparent distance of the fish, concluding that it appears to be 84 cm in front of the mask, contrary to initial calculations that suggested 1.25 m. The correct application of the formula n1/s + n2/s' = (n2 - n1)/r is crucial for accurate results.

PREREQUISITES
  • Understanding of optics, specifically refraction and lens equations.
  • Familiarity with the lens maker's equation and its components.
  • Knowledge of the refractive indices of air (n1=1) and water (n2=1.33).
  • Basic algebra skills for solving equations and manipulating variables.
NEXT STEPS
  • Study the derivation and applications of the lens maker's equation.
  • Explore the principles of refraction and how they apply to different mediums.
  • Investigate the effects of curvature on lens optics and image formation.
  • Learn about practical applications of optics in underwater environments, such as in diving and photography.
USEFUL FOR

Students studying physics, particularly in optics, scuba divers interested in understanding visual perception underwater, and educators teaching concepts related to refraction and lens behavior.

pyroknife
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Homework Statement



On a vacation, you are scuba-diving and using a diving mask that has a
face plate and that bulges outward with a radius of curvature of 0.50 m. As a
result, a convex spherical surface exists between the water and the air in the
mask. A fish swims by you 2.5 m in front of your mask. (a) How far in front of
the mask does the fish appear to be?

Homework Equations


n1/s+n2/s'=(n2-n1)/r


The Attempt at a Solution


The viewer is obviously inside the diving mask, so we make everything with respect to that.
n1=1, n2=1.33, s=-2.5 (since the object is located on the other side of the faceplate), r=.5. That however is not getting me the right answer. What am I doing wrong?
 
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You should show your work, then perhaps someone can see where you did go wrong. Also, it is courteous to provide the answer with the question, given that you have it.
 
With those #s I got 1.25m (which would mean that the image appears to be in the faceplate, doesn't make sense) , the answer is -84cm (the fish appears to be in front of your mask)
 

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