Resolving Power
Magnification is useless past a point: what matters is how fine a detail can be separated.
Lesson at a glanceShow the key points
- Microscope: resolving power = 1/(smallest separation just resolved) = 2μ sin θ/λ, where θ is the angle a radius of the objective subtends at the object.
- Oil immersion raises μ between object and objective, raising the resolving power.
- Telescope: resolving power = 1/(smallest angular separation) = a/1.22λ, a = diameter of the objective.
- So astronomical telescopes have apertures of a metre or more.
You can always build a microscope or telescope with more magnification. But past a point it only shows a bigger blur. The real limit is set by diffraction: how close two details can be and still look like two.
Why there’s a limit
As we saw in the chapter on light waves, every lens images a point as a small diffraction disc. Two points closer than about one disc radius merge. Magnifying merges discs just as much as it magnifies them.
Resolving power of a microscope
The resolving power of a microscope is the reciprocal of the smallest distance between two points that it can just resolve. It depends on the wavelength λ, the refractive index μ of the medium between the object and the objective, and the angle θ that a radius of the objective subtends at the object:
To raise it, specimens are viewed with a drop of oil filling the gap between them and the objective. This oil immersion increases μ.
Resolving power of a telescope
For a telescope, it is the reciprocal of the smallest angle between two distant objects that can just be resolved:
That is why astronomical telescopes have objectives a metre or more across.
An objective with θ = 60° is used with oil of μ = 1.5 and light of 500 nm. What is the smallest separation it can resolve?
A telescope mirror 2.4 m across observes at 550 nm. What is the smallest angle it can resolve?
- 1Diffraction, not magnification, limits how much detail an instrument shows.
- 2Microscope: R = 2μ sin θ/λ; oil immersion raises μ.
- 3Telescope: R = a/1.22λ; bigger objectives resolve smaller angles.
Check yourself
Keep exploring
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