{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"telescope-magnification"},"result":{"entity_type":"calculator","id":"telescope-magnification","calculator_id":"telescope-magnification","canonical_url":"https://tttkmbb.com/photography/telescope-magnification","name":"Telescope Magnification Calculator","title":"Telescope Magnification Calculator – Power, Exit Pupil, True Field of View and Resolution","category":"photography","category_name":"Photography & Optics","tool_name":"calculate_telescope_magnification","featured_mcp_tool":false,"description":"Computes the magnification of a telescope and eyepiece combination (with optional Barlow), the exit pupil, true field of view, focal ratio, useful magnification range, Dawes and Rayleigh resolution limits and an estimated limiting magnitude.","use_when":"You are choosing an eyepiece or Barlow for a telescope and want to know the resulting power, field of view and whether the magnification is useful for the aperture.","do_not_use_when":"You need the angle of view of a camera lens (use field-of-view) or exposure settings for astrophotography.","inputs":[{"name":"telescope_focal_length_mm","label":"Telescope focal length","type":"number","unit":"mm","required":true,"min":50,"max":20000,"description":"Focal length of the telescope objective or mirror.","example":1200},{"name":"eyepiece_focal_length_mm","label":"Eyepiece focal length","type":"number","unit":"mm","required":true,"min":1,"max":100,"description":"Focal length of the eyepiece.","example":10},{"name":"aperture_mm","label":"Aperture","type":"number","unit":"mm","required":true,"min":10,"max":5000,"description":"Clear aperture (objective or primary mirror diameter).","example":200},{"name":"barlow_factor","label":"Barlow / reducer factor","type":"number","required":false,"default":1,"min":0.2,"max":10,"description":"Magnification of a Barlow lens (2, 3) or focal reducer (0.63); 1 for none.","example":1},{"name":"eyepiece_afov_degrees","label":"Eyepiece apparent field of view","type":"number","unit":"°","required":false,"default":50,"min":20,"max":120,"description":"Apparent field of view of the eyepiece design (Plössl 50°, wide-field 68–82°, ultra-wide 100°).","example":50}],"outputs":[{"name":"magnification","label":"Magnification","type":"number","unit":"×","decimals":1,"description":"telescope focal length × barlow_factor / eyepiece focal length."},{"name":"effective_focal_length_mm","label":"Effective focal length","type":"number","unit":"mm","decimals":0,"description":"Telescope focal length × Barlow factor."},{"name":"exit_pupil_mm","label":"Exit pupil","type":"number","unit":"mm","decimals":2,"description":"aperture / magnification; above ~7 mm the eye cannot use all the light, below ~0.5 mm the image is dim."},{"name":"true_field_of_view_degrees","label":"True field of view","type":"number","unit":"°","decimals":3,"description":"Eyepiece apparent field / magnification (the full Moon is about 0.5°)."},{"name":"focal_ratio","label":"Focal ratio","type":"number","decimals":2,"description":"Native f-number = telescope focal length / aperture."},{"name":"max_useful_magnification","label":"Maximum useful magnification","type":"number","unit":"×","decimals":0,"description":"Rule of thumb 2 × aperture in mm (50× per inch); beyond it the image only gets larger and dimmer."},{"name":"min_useful_magnification","label":"Minimum useful magnification","type":"number","unit":"×","decimals":0,"description":"aperture / 7 mm, the power at which the exit pupil equals a dark-adapted eye pupil."},{"name":"dawes_limit_arcsec","label":"Dawes limit","type":"number","unit":"arcsec","decimals":2,"description":"116 / aperture_mm: closest double star the telescope can split (empirical)."},{"name":"rayleigh_limit_arcsec","label":"Rayleigh limit","type":"number","unit":"arcsec","decimals":2,"description":"138 / aperture_mm: diffraction-limited resolution for 550 nm light."},{"name":"limiting_magnitude","label":"Limiting magnitude","type":"number","unit":"mag","decimals":1,"description":"7.5 + 5·log10(aperture in cm): faintest star visible under dark skies (rule of thumb)."}],"input_schema":{"type":"object","properties":{"telescope_focal_length_mm":{"description":"Focal length of the telescope objective or mirror. Unit: mm.","type":"number","minimum":50,"maximum":20000,"examples":[1200],"x-unit":"mm"},"eyepiece_focal_length_mm":{"description":"Focal length of the eyepiece. Unit: mm.","type":"number","minimum":1,"maximum":100,"examples":[10],"x-unit":"mm"},"aperture_mm":{"description":"Clear aperture (objective or primary mirror diameter). Unit: mm.","type":"number","minimum":10,"maximum":5000,"examples":[200],"x-unit":"mm"},"barlow_factor":{"description":"Magnification of a Barlow lens (2, 3) or focal reducer (0.63); 1 for none.","type":"number","minimum":0.2,"maximum":10,"default":1,"examples":[1]},"eyepiece_afov_degrees":{"description":"Apparent field of view of the eyepiece design (Plössl 50°, wide-field 68–82°, ultra-wide 100°). Unit: °.","type":"number","minimum":20,"maximum":120,"default":50,"examples":[50],"x-unit":"°"}},"additionalProperties":false,"required":["telescope_focal_length_mm","eyepiece_focal_length_mm","aperture_mm"]},"output_schema":{"type":"object","properties":{"magnification":{"description":"telescope focal length × barlow_factor / eyepiece focal length. Unit: ×.","type":"number","x-unit":"×"},"effective_focal_length_mm":{"description":"Telescope focal length × Barlow factor. Unit: mm.","type":"number","x-unit":"mm"},"exit_pupil_mm":{"description":"aperture / magnification; above ~7 mm the eye cannot use all the light, below ~0.5 mm the image is dim. Unit: mm.","type":"number","x-unit":"mm"},"true_field_of_view_degrees":{"description":"Eyepiece apparent field / magnification (the full Moon is about 0.5°). Unit: °.","type":"number","x-unit":"°"},"focal_ratio":{"description":"Native f-number = telescope focal length / aperture.","type":"number"},"max_useful_magnification":{"description":"Rule of thumb 2 × aperture in mm (50× per inch); beyond it the image only gets larger and dimmer. Unit: ×.","type":"number","x-unit":"×"},"min_useful_magnification":{"description":"aperture / 7 mm, the power at which the exit pupil equals a dark-adapted eye pupil. Unit: ×.","type":"number","x-unit":"×"},"dawes_limit_arcsec":{"description":"116 / aperture_mm: closest double star the telescope can split (empirical). Unit: arcsec.","type":"number","x-unit":"arcsec"},"rayleigh_limit_arcsec":{"description":"138 / aperture_mm: diffraction-limited resolution for 550 nm light. Unit: arcsec.","type":"number","x-unit":"arcsec"},"limiting_magnitude":{"description":"7.5 + 5·log10(aperture in cm): faintest star visible under dark skies (rule of thumb). Unit: mag.","type":"number","x-unit":"mag"}}},"formula":"magnification = telescope_focal_length_mm × barlow_factor / eyepiece_focal_length_mm; exit_pupil_mm = aperture_mm / magnification; true_field = eyepiece_afov_degrees / magnification; dawes = 116 / aperture_mm; rayleigh = 138 / aperture_mm; limiting_magnitude = 7.5 + 5·log10(aperture_mm / 10)","method":"Geometric optics for visual use; the true field is approximate for wide-field eyepieces (field-stop method is exact). Resolution limits assume perfect optics and steady seeing, which typically caps resolution at 1–2 arcsec.","sources":[{"name":"Wikipedia – Dawes' limit","url":"https://en.wikipedia.org/wiki/Dawes%27_limit","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Exit pupil","url":"https://en.wikipedia.org/wiki/Exit_pupil","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Limiting magnitude","url":"https://en.wikipedia.org/wiki/Limiting_magnitude","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"200 mm f/6 Newtonian (1200 mm) with a 10 mm eyepiece","inputs":{"telescope_focal_length_mm":1200,"eyepiece_focal_length_mm":10,"aperture_mm":200},"expected":{"magnification":120,"exit_pupil_mm":1.67,"true_field_of_view_degrees":0.417,"focal_ratio":6,"max_useful_magnification":400,"dawes_limit_arcsec":0.58,"limiting_magnitude":14},"url":"https://tttkmbb.com/api/v1/calculate/telescope-magnification?telescope_focal_length_mm=1200&eyepiece_focal_length_mm=10&aperture_mm=200"},{"name":"Same telescope with a 2× Barlow","inputs":{"telescope_focal_length_mm":1200,"eyepiece_focal_length_mm":10,"aperture_mm":200,"barlow_factor":2},"expected":{"magnification":240,"exit_pupil_mm":0.83,"true_field_of_view_degrees":0.208,"effective_focal_length_mm":2400},"url":"https://tttkmbb.com/api/v1/calculate/telescope-magnification?telescope_focal_length_mm=1200&eyepiece_focal_length_mm=10&aperture_mm=200&barlow_factor=2"}],"faq":[{"q":"Why is more magnification not always better?","a":"Magnification also enlarges the diffraction blur and dims the image; above about 2× the aperture in mm (or an exit pupil below 0.5 mm) no further detail appears. Atmospheric seeing usually limits usable power to 200–300×."},{"q":"What does the true field of view tell me?","a":"The angular width of sky visible in the eyepiece. 0.417° is smaller than the full Moon (0.5°), so at 120× the Moon does not fit in the view."}],"tags":["telescope magnification","eyepiece","exit pupil","true field of view","dawes limit","barlow"],"related":[{"calculator_id":"field-of-view","reason":"Angle of view of a camera lens on a sensor."},{"calculator_id":"angle","reason":"Convert between degrees, arcminutes and arcseconds."}],"links":{"html":"https://tttkmbb.com/photography/telescope-magnification","markdown":"https://tttkmbb.com/photography/telescope-magnification.md","json":"https://tttkmbb.com/photography/telescope-magnification.json","api":"https://tttkmbb.com/api/v1/calculate/telescope-magnification","schema":"https://tttkmbb.com/api/v1/calculators/telescope-magnification","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:50:42Z"}