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

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A diving mask with a convex spherical surface alters the perceived distance of underwater objects due to the refraction of light. In this scenario, a fish 2.5 m away appears to be at a different distance when viewed through the mask, which has a radius of curvature of 0.50 m. The correct application of the lens formula reveals that the fish appears to be 84 cm in front of the mask, not the initially calculated 1.25 m. The discrepancy arises from misapplying the sign conventions in the lens formula. Understanding the refraction principles is crucial for accurate distance perception underwater.
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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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