The Telescope
Simple Explanation
An astronomical telescope also uses two converging lenses, but arranged to magnify distant objects instead of nearby tiny ones — its magnifying power is simply the ratio of the two lenses' focal lengths, M=f₀/fₑ.
Why Do We Need It?
Telescopes let us see details in objects — the Moon's craters, the rings of Saturn, distant galaxies — that are impossibly far away, using exactly the same two-lens principle as a microscope but tuned for distant rather than tiny objects.
See It
Two vertical lines representing a long-focal-length objective lens on the left and a short-focal-length eyepiece lens on the right, both centered on the same optical axis
Formula
Astronomical Telescope Magnifying Power
M = f₀/fₑ
A telescope's magnifying power is simply the ratio of its objective lens's focal length to its eyepiece lens's focal length — a longer objective or a shorter eyepiece both increase magnification.
- M
- — magnifying power (dimensionless)
- f₀
- — focal length of the objective lens, in metres (m)
- fₑ
- — focal length of the eyepiece lens, in metres (m)
When to use it: Whenever a telescope's magnifying power needs to be found from its two lenses' focal lengths.
Worked Example
Find a telescope's magnifying power
A telescope has an objective lens of focal length 1.0 m and an eyepiece of focal length 0.02 m (20 mm). Find its magnifying power.
Why Does This Work?
A long-focal-length objective forms a large real image of a distant object at its focal point; the short-focal-length eyepiece then acts as a powerful magnifying glass on that image — the shorter the eyepiece's focal length relative to the objective's, the larger the final magnification.
Real-Life Example
Amateur astronomers choosing eyepieces
Amateur astronomers often own several interchangeable eyepieces with different focal lengths for the same telescope.
Swapping in an eyepiece with a shorter focal length directly increases M=f₀/fₑ, letting the same telescope zoom in more (at the cost of a dimmer, narrower field of view).
Practice
A telescope has f₀=0.8 m and fₑ=0.025 m. Find its magnifying power.
HardCommon mistake
Assuming a bigger telescope objective automatically means much more magnification — magnification depends on the RATIO f₀/fₑ, not the objective's size alone; a larger objective mainly improves light-gathering and image brightness, not just magnification.
Quick Review
- M = f₀/fₑ.
- Long objective focal length or short eyepiece focal length both increase magnification.
- Same two-lens principle as a microscope, tuned for distant rather than tiny objects.