JEE MainPhysicsRay Optics
A researcher is observing a biological specimen using a compound microscope. Initially, the observation is made in air ( ₁ = 1.0 ) using light of wavelength 600 nm . To improve the clarity, the researcher switches to an oil immersion objective where the medium between the object and the lens has a refractive index ₂ = 1.5 , and simultaneously changes the light source to one emitting at a wavelength of 400 nm . The ra
Options
- A4:9
- B3:2
- C2:3
- D9:4
Correct answer
D. 9:4
Step-by-step solution
The resolving power (R.P.) of a compound microscope is given by: R.P. = 2 Thus, R.P. . Let the initial resolving power be R.P. ₁ and the new resolving power be R.P. ₂ . We can write the ratio as: R.P. ₂ R.P. ₁ = ( ₂ ₁ ) ( ₁ ₂ ) Substituting the given values: ₁ = 1.0 , ₁ = 600 nm ₂ = 1.5 , ₂ = 400 nm R.P. ₂ R.P. ₁ = ( 1.5 1.0 ) ( 600 400 ) = 1.5 1.5 = 2.25 Converting 2.25 to a fraction gives 9 4 . Therefore, the ratio is 9:4 . Answer: 9:4