A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is , calculate the change of microscope's resolving power due to oil and choose the correct option
- (A)Resolving power will be in the oil than it was in the air
- (B)Resolving power will be twice in the oil than it was in the air.✓ Correct
- (C)Resolving power will be four times in the oil than it was in the air.
- (D)Resolving power will be in the oil than it was in the air.
Answer: (B)
Solution
The resolving power of a microscope is proportional to its numerical aperture, which carries the refractive index of the medium between the object and the objective: , where is the wavelength measured in air. Immersing the instrument in oil changes nothing in this expression except the index , which rises from to . Because the resolving power depends on to the first power, doubling the refractive index of the medium simply doubles the resolving power, so in the oil it becomes twice what it was in air.
JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option