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Question:

A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens?

Solution:

Given: nl = 1.65, ng = 1.5
It is clear that nl > ng. Therefore, nl/ng < 1.
In this condition, 1/fl = (nl/ng - 1)(1/R1 - 1/R2), where fl is the focal length of the lens in the medium, R1 and R2 are the radii of curvature of the lens surfaces.
Since nl/ng < 1, 1/fl < 0, which means fl is negative. This indicates that the nature of the lens will change; the concave lens will behave like a convex lens.