SaitechAI — Concave Mirror Calculator
Concept: Minimum distance between object and its real image of a concave mirror
Timer: 00:00
Session: —
Calculator (Use magnitudes in cm; concave mirror)
Formula:
Minimum separation is 4f (when u = v = 2f).
1/f = 1/u + 1/v ⇒ v = (f·u)/(u − f); separation S = u + v.Minimum separation is 4f (when u = v = 2f).
Prefill examples:
Practice — 6 Questions
Solve, then verify with the calculator above. (Use cm.)
1) A concave mirror has f = 10. If the object is at u = 18, find the image distance v and the object–image separation S. Check whether \(S \ge 4f\).
Show Key
v = (10×18)/(18−10) = 22.5; S = 18 + 22.5 = 40.5 ≥ 4f (=40).
2) For f = 8, at what object distance is the separation minimum? Find the minimum separation.
Show Key
Minimum at u = 2f = 16 and v = 16; Smin = 4f = 32.
3) A mirror with f = 12 forms a real image at distance v. If the object is at u = 30, compute v, S, and compare with 4f.
Show Key
v = (12×30)/(30−12) = 20; S = 30 + 20 = 50 ≥ 48; difference = 2.
4) For f = 15 and u = 25, find v, S. Is the separation close to the minimum?
Show Key
v = (15×25)/(25−15) = 37.5; S = 62.5; 4f = 60 ⇒ slightly above minimum.
5) If the required separation is exactly 4f for a mirror with f = 18, where should you place the object, and where will the image form?
Show Key
Place at u = 2f = 36; image also at v = 36; S = 72 = 4f.
6) A student places an object at u = 28 before a mirror with f = 20. Calculate v and S; comment on how much more than the minimum the separation is.
Show Key
v = (20×28)/(28−20) = 70; S = 98; 4f = 80 ⇒ 18 cm more than minimum.
© SaitechAI • Use Cartesian magnitudes for this tool (concave mirror, real object → real image).