The Short Answer
The total magnification is 400x because a compound microscope magnifies in two stages, and the stages multiply. The 40x objective forms an image of the specimen 40 times larger than life. The 10x eyepiece then enlarges that image a further 10 times. So 40 × 10 = 400x.
The 400x figure assumes a 10x eyepiece, which is the standard on most microscopes. With a different eyepiece, the total changes.
Why the Two Numbers Multiply
It can seem odd that the numbers multiply rather than add. The reason is that the eyepiece is not looking at the specimen. It is looking at an image that has already been magnified.
Stage one: the objective
Light passes through the specimen and into the objective. The objective forms a real, inverted, enlarged image inside the microscope tube, at a position called the intermediate image plane. With a 40x objective, a feature 10 µm across in the specimen becomes 400 µm (0.4 mm) across in that intermediate image.
Stage two: the eyepiece
The eyepiece works like a magnifying glass held over that intermediate image. A 10x eyepiece makes the 0.4 mm image appear ten times larger to your eye, so the original 10 µm feature now looks the same size as a 4 mm object would when viewed from a standard reading distance of about 25 cm.
10 µm became 4 mm: that is 400 times larger.
Think of it like photocopying with enlargement. If you enlarge a picture to 4 times its size, then enlarge the copy to 10 times its size, the final copy is 40 times larger than the original, not 14. Each stage scales everything the previous stage produced.
What If Your Eyepiece Is Not 10x?
The same 40x objective gives different totals with different eyepieces:
| Eyepiece | With 40x objective |
|---|---|
| 5x | 200x |
| 10x | 400x |
| 15x | 600x |
| 20x | 800x |
Some microscopes also have an additional magnification factor built into the head or a magnification changer. If so, multiply by that too. Our guide to calculating total magnification covers these extra factors, and how to find the total magnification of a compound microscope gives a step-by-step routine for reading your own lenses.
Is 400x Actually Useful With a 40x Objective?
Yes. A typical 40x objective has a numerical aperture (NA) of about 0.65, often engraved as “40/0.65”. A widely used rule of thumb says total magnification is most useful between about 500 and 1000 times the NA. For NA 0.65, that is roughly 325x to 650x.
- 400x (10x eyepiece) sits comfortably inside that range.
- 600x (15x eyepiece) is still inside it, near the upper end.
- 800x (20x eyepiece) goes past it. The image gets bigger, but it is unlikely to show more detail. This is called empty magnification.
To see real additional detail beyond what the 40x objective provides, you generally need an objective with higher NA, such as a 100x oil immersion objective. The relationship between the two ideas is explained in magnification vs resolution.
Is “40x” the Same as “400x”?
They are often used loosely, but they mean different things:
- “40x” usually refers to the objective lens’s own magnification.
- “400x” is the total magnification you see through a 10x eyepiece.
So if someone says they are “on 40x”, they usually mean the 40x objective, which normally gives 400x total. If a microscope’s listing says “40x to 1000x”, it is describing total magnification, from the 4x objective up to the 100x objective, each with a 10x eyepiece.
What You Can See at 400x
At 400x with a typical brightfield microscope, the field of view is roughly 0.45 to 0.55 mm across, depending on the eyepiece’s field number (see field of view). Depending on the specimen and its preparation, you can often see:
- Individual cells in plant and animal tissue
- Cell walls, and often chloroplasts in plant cells
- Nuclei in many stained cells
- Single-celled organisms in pond water in reasonable detail
- Bacteria as very small specks, usually without clear shape
For good results, raise the condenser close to the slide, adjust its aperture diaphragm, and use the fine focus only. The depth of field at 400x is shallow, so slowly focusing up and down helps you see the full structure.