Telescope & Microscope: Compound Optics Lab
Switch between a telescope and a compound microscope, adjust the objective and eyepiece focal lengths, and watch the ray-traced image and total magnification update live.
Switch between telescope and microscope mode, then change the objective and eyepiece focal lengths and watch the total magnification and the real ray-traced image update live.
About the Telescope & Microscope: Compound Optics Lab
Free telescope & microscope: compound optics lab. Switch between a telescope and a compound microscope, adjust the objective and eyepiece focal lengths, and watch the ray-traced image and total magnification update live. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the telescope & microscope: compound optics lab runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Switch between a telescope and a compound microscope, adjust the objective and eyepiece focal lengths, and watch the ray-traced image and total magnification update live. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Telescope & Microscope: Compound Optics Lab
- Use the controls to change Objective focal length f₀, Eyepiece focal length fₑ. The simulation reacts instantly.
- Pick an option such as Telescope, Microscope to switch modes or load an example.
- Press "Reset to defaults", "Lab Report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Build a 20x telescope using the challenge.
- Switch to microscope mode and move the object just outside the focal length.
- Compare a short eyepiece versus a long one in telescope mode.
- Work out the microscope's total magnification by hand before checking the readout.
Key ideas you can learn
- A telescope's angular magnification is M = f0/fe: a long objective focal length combined with a short eyepiece focal length gives high magnification.
- A compound microscope's objective first forms a real, magnified intermediate image (found from the thin lens equation), which the eyepiece then magnifies again as a simple magnifier.
- Total microscope magnification is the product of the objective's linear magnification and the eyepiece's angular magnification, M = |mo x me|.
- Both instruments use two converging lenses, but a telescope's object is effectively at infinity while a microscope's object sits just outside the objective's focal length.
Show my work
Challenges
Challenge 1 - build a 20x telescope
In telescope mode, angular magnification is M = f₀/fₑ. Keep f₀ = 50 cm and set fₑ so the magnification is exactly 20×. Enter the eyepiece focal length you used, in centimeters.
Challenge 2 - microscope total magnification
Switch to microscope mode with f₀ = 1 cm, fₑ = 2.5 cm and object distance d₀ = 1.2 cm. First find the objective's image distance from 1/f₀ = 1/d₀ + 1/dᵢ, then the objective magnification mₒ = −dᵢ/d₀, then the eyepiece angular magnification mₑ = 25/fₑ (near point 25 cm). Enter the total magnification M = mₒ × mₑ (magnitude).
Where this is used in the real world
Astronomers size telescope eyepieces exactly this way to hit a target magnification, and biology and materials labs use compound microscopes built from exactly this two-lens design.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why does a telescope need a long objective and short eyepiece for high magnification?
Telescope magnification is M = f0/fe, so increasing the objective's focal length or decreasing the eyepiece's focal length both directly increase the ratio and therefore the magnification.
Why is a microscope's total magnification a product of two magnifications rather than a simple ratio?
The objective first creates a real intermediate image with its own linear magnification mo, and the eyepiece then magnifies that already-enlarged image again as a simple magnifier with angular magnification me, so the two multiply together.
Is the Telescope & Microscope: Compound Optics Lab free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Telescope & Microscope: Compound Optics Lab work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.