Change in focal length of lens when immersed in water formula
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Why, when a lens is immersed in water, does its focal length increase?
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Tristan Hubsch, Professor at Howard University (1992-present)
Answered Feb 8, 2017
Plenty of good answers already to this great question, but let me add:
A.: Because the ratio of the refractive indices of the lens and its surroundings (on both sides) is closer to 1.
To see how this matters, consider the following sequence of thought experiments (which actually can be backed up by real experiments):
While the lens is immersed in the water and light (laser-pointer, for convenience) beams are set to pass through it to mark the focal point, add salt, sugar or some other material that is easily soluble but does not change the translucency of water. Observe it the focal length changes.
In the (now really thought-experiment fashion) extreme limit when the glas lens is surrounded by glass itself, there will be no refraction, and the focal length tends to ∞∞.
Now turn this around, and imagine the material of the lens to be replaceable. For starters, suppose that the lens is a rigid container of negligibly thin translucent walls filled with… water. Again, there will be no focusing; the focal length will be ∞∞.
Finally, consider the previous lens-container, submerged in water, and filled with… air. Now the same lens will diverge the beams of light!
A sequence of thought-experiments like this should help understand that the focal length and even convergent/divergent nature of the lens depends on the ratio of the refractive indices (optical “density”) of the materials of the lens and its surroundings.
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9 ANSWERS

Tristan Hubsch, Professor at Howard University (1992-present)
Answered Feb 8, 2017
Plenty of good answers already to this great question, but let me add:
A.: Because the ratio of the refractive indices of the lens and its surroundings (on both sides) is closer to 1.
To see how this matters, consider the following sequence of thought experiments (which actually can be backed up by real experiments):
While the lens is immersed in the water and light (laser-pointer, for convenience) beams are set to pass through it to mark the focal point, add salt, sugar or some other material that is easily soluble but does not change the translucency of water. Observe it the focal length changes.
In the (now really thought-experiment fashion) extreme limit when the glas lens is surrounded by glass itself, there will be no refraction, and the focal length tends to ∞∞.
Now turn this around, and imagine the material of the lens to be replaceable. For starters, suppose that the lens is a rigid container of negligibly thin translucent walls filled with… water. Again, there will be no focusing; the focal length will be ∞∞.
Finally, consider the previous lens-container, submerged in water, and filled with… air. Now the same lens will diverge the beams of light!
A sequence of thought-experiments like this should help understand that the focal length and even convergent/divergent nature of the lens depends on the ratio of the refractive indices (optical “density”) of the materials of the lens and its surroundings.
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