Focus of Lens Submerged In Water

AI Thread Summary
A glass lens with a power of +5.2 diopters in air has a power of approximately 1.3 diopters when submerged in water. The solution involves using Snell's Law to determine the effective refractive index by dividing the lens's refractive index (1.50) by that of water (1.33). The derivation of the Lensmaker's Equation confirms this result, with the calculation yielding a power adjustment based on the surrounding medium. The key takeaway is that the refractive index ratio is crucial for accurately determining the lens's power in different environments. Understanding these principles is essential for solving similar optics problems.
JSGandora
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Homework Statement


A glass lens (n=1.50) in air has a power of +5.2 diopters. What would its power be if it were submerged in water?

Homework Equations


Not too sure. May be Lensmaker's Equation, Snell's Law, and Power of a Lens Equation.

The Attempt at a Solution


I'm trying to derive the Lensmaker's Equation with the surrounding substance having index of refraction 1.33 but that didn't work. I also tried changing the index of refraction of the lens so that it was with respect to the speed of light in water rather than in air.
 
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Haha, I found it.

I have found the solution to be 1.3 diopters. You just divide the refractive index of the lens by that of the water to get the effective refractive index from Snell's Law. That derivation of the Lensmaker's equation holds true so we get \left(\frac{1.5}{1.33}-1\right)(10.4)\approx \boxed{1.3D}. I got the same concept last night without knowing that it was correct because I didn't subtract 1 from the ratio of refractive indices. >.<
 
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