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Question:

Under what condition does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid?

Solution:

When a convex lens is immersed in a liquid, its focal length is given by:

1/fl = (nl - 1)(1/R1 - 1/R2)

where:

  • fl is the focal length of the lens in the liquid
  • nl is the refractive index of the lens relative to the liquid
  • R1 and R2 are the radii of curvature of the lens surfaces.

A convex lens will behave as a plane glass plate when its focal length approaches infinity (fl = ∞) or when 1/fl = 0. This is possible only when:

nl = 1

Since nl = ng/nl (where ng is the refractive index of the glass and nl is the refractive index of the liquid), the condition for the lens to behave as a plane glass plate is:

ng = nl

It means the refractive index of the lens (glass) must be equal to the refractive index of the liquid.