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JEE MainPhysicsRay Optics

A microscope operates in two different configurations to observe a specimen. In the first configuration, the objective lens is in air, the wavelength of light used is 600 nm , and the semi-vertical angle of the cone of light entering the objective is 30^ . In the second configuration, the objective is immersed in an oil of refractive index 1.5 , the wavelength of light used is 400 nm , and the semi-vertical angle is

Options

  1. A4 9 3
  2. B9 4
  3. C9 3 4
  4. D9 2

Correct answer

C. 9 3 4

Step-by-step solution

The limit of resolution x of a microscope is given by x = 1.22 2 . Thus, x . For the first configuration: ₁ = 600 nm , ₁ = 1 , ₁ = 30^ x₁ 600 1 30^ = 600 0.5 = 1200 For the second configuration: ₂ = 400 nm , ₂ = 1.5 , ₂ = 60^ x₂ 400 1.5 60^ = 400 1.5 3 2 = 1600 3 3 Taking the ratio of the two limits of resolution: x₁ x₂ = 1200 1600 3 3 = 1200 3 3 1600 = 3 4 3 3 = 9 3 4 Answer: 9 3 4

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