The Simple Microscope (Magnifier)
A short-focus lens lets you hold things closer than your eye could manage.
Lesson at a glanceShow the key points
- Naked eye: largest angle θ₀ = h/D, object at the near point.
- Object at the focus of a lens (f < D): rays enter parallel, angle θ = h/f. Image at infinity: normal adjustment, eye relaxed.
- Magnifying (angular) power m = θ/θ₀ = D/f (19.1).
- Object moved closer so the virtual image is at the near point: m = D/u₀ = 1 + D/f (19.2).
- Aberrations limit a simple magnifier to about 4×; written with the unit × (a 10× magnifier).
To see something small, you bring it closer, until your eye can no longer focus. A magnifying glass lets you bring it closer still.
The naked-eye limit
The largest angle an object of height h can subtend while still in focus is when it is at the near point:
Adding a lens
Place a converging lens of focal length f (less than D) just in front of the eye, and put the object at its focus. Rays from each point of the object leave the lens parallel, as if from an image at infinity, which the relaxed eye focuses easily. The angle at the eye is
Since f < D, θ > θ₀: the retinal image is bigger. A converging lens used this way is a simple microscope or magnifier. With the image at infinity, the eye is in normal adjustment.
Image at the near point
Move the object a little closer, to u₀, so the virtual image forms at the near point (v = −D). The eye strains, but sees more detail. From the lens formula, , and the angle is h/u₀:
A magnifier has focal length 8.0 cm. Find its magnifying power (a) with the eye relaxed, (b) with the image at 25 cm.
An 8 D lens is used as a magnifier for the greatest magnification. Where should the object be?
- 1Naked eye at best: θ₀ = h/D.
- 2Object at the focus of a magnifier: θ = h/f, m = D/f (eye relaxed).
- 3Image at the near point: m = 1 + D/f.
- 4Single-lens magnifiers are useful up to about 4×.
Check yourself
Keep exploring
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