A microscope is used to resolve two closely spaced points. Initially, the objective is in air and light of wavelength 600 nm is used. The setup is then immersed in a transparent liquid and light of wavelength 400 nm is used. If the limit of resolution in the liquid becomes one-third of its initial value in air, the refractive index of the liquid is:

Step-by-step solution

The limit of resolution d of a microscope is given by d = 1.22 2 . Thus, d . Let the initial limit of resolution in air be d₁ and the final limit of resolution in the liquid be d₂ . We are given d₂ d₁ = 1 3 , ₁ = 600 nm , ₂ = 400 nm , and ₁ = 1 . Using the proportionality, we have: d₂ d₁ = ( ₂ ₁ ) ( ₁ ₂ ) Substituting the given values: 1 3 = ( 400 600 ) ( 1 ₂ ) 1 3 = 2 3 ₂ ₂ = 2.0 Answer: 2.0