University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 34 - Geometric Optics - Problems - Discussion Questions - Page 1151: Q34.17

Answer

The focal length increases.

Work Step by Step

We assume that the index of refraction of the glass is still greater than that of water, which is typical. Pages 1130-1131 derive the lensmaker’s equation for a lens in air, and invite you to do the same for a lens immersed in a material with index of refraction greater than air’s. You should do that to verify this answer, but here, let’s resort to a physical argument. When light travels from air into a glass lens, or vice versa, it will bend by a greater amount than if the lens were immersed in water. This is because of the relatively large ratio of $\frac{n_{glass}}{n_{air}}$. When the lens is immersed in water, the ratio of $\frac{n_{glass}}{n_{water}}$ is not as great, so the bending is more gentle. Therefore, the rays come to a focus farther away from the lens, resulting in a larger f.
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