Optics
Astronomical telescope
Afocal lenses are separated by f_objective + f_eyepiece; M = −f_objective/f_eyepiece is the angular magnification for a distant object, while the on-bench image of a near object shows the lateral magnification f_eyepiece/f_objective.
Astronomical telescope — interactive Optics simulation. Two converging lenses share a focus; the angular magnification is M = −f_objective/f_eyepiece. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Astronomical telescope
An afocal telescope separates its lenses by f_objective + f_eyepiece; M = −f_objective/f_eyepiece.
The objective's focal plane coincides with the eyepiece's focal plane, so the lens separation is f_objective + f_eyepiece and parallel input leaves parallel. The angular magnification is the focal-length ratio; its negative sign indicates inversion.
- M = −f_obj/f_eye
- Angular magnification
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
An afocal (Keplerian) telescope places its objective and eyepiece so their focal points coincide — parallel light in, parallel light out. Does a shorter eyepiece focal length give higher or lower telescope magnification?
Predictions to weigh
- A shorter eyepiece gives lower magnification.
- Eyepiece focal length doesn't affect magnification.
- Higher — magnification is the ratio of objective to eyepiece focal length, so shrinking the eyepiece's focal length increases the ratio.
Variable roles
What you set:
- Eyepiece focal length f_e (cm)
What you measure:
- Angular magnification M
How the investigation runs
- Open the telescope preset and press Reset. The objective has f = 100 cm; the two lenses are separated by their combined focal lengths (afocal condition).
- Enable the angular-magnification readout.
- Set the eyepiece's focal length for each trial (objective fixed at f = 100 cm) and record the resulting magnification.
Governing equation
Telescope Angular Magnification — M = −f_o/f_e
An afocal Keplerian telescope's angular magnification is M = −f_o/f_e, the ratio of the objective's focal length to the eyepiece's. A longer objective or shorter eyepiece both increase magnification.
What the printable worksheet asks students to work out
- For one trial, compute M = −f_o/f_e using f_o = 100 cm. Compare to the table.
- Explain why the magnification is negative (an inverted image, typical of a simple Keplerian telescope) and why a shorter eyepiece focal length increases the magnitude of M.
Where this shows up beyond the lab
- Unlike the eyepiece (which sets magnification), the OBJECTIVE lens's diameter (not shown in this focal-length-only model) determines how much light the telescope gathers and its ultimate resolving power. Explain why astronomers care more about a telescope's aperture (objective diameter) than its magnification alone.
- 'Afocal' means parallel light in produces parallel light out — the telescope has no single overall focal length itself, unlike a camera lens or magnifying glass. Explain why this design is ideal for viewing very distant objects (effectively at infinity) with a relaxed eye.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Telescope
- Select the objective lens
- Press Play
- Angular size of distant objects
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.