Projection versus wide-angle viewing
With do = 75 cm and equal 25 cm magnitudes, the concave option forms a real inverted image at 37.5 cm while the convex option forms a smaller upright virtual image at -18.75 cm.
Physics and geometric optics
Mirror Scenario Calculator
Compare two spherical-mirror choices for the same object, including signed image location, magnification, orientation, and screen feasibility.
Two-mirror decision comparison
Compare two mirror outcomes on one controlled object basis
This calculator keeps object geometry fixed while solving two mirror choices independently. It then compares scale and screen feasibility without turning virtual-image distance into a false screen location.
Scenario A image distance-
Scenario B image distance-
Scenario A magnification-
Absolute scale ratio A/B-
Current model evidence
Controlled mirror-comparison ledger
Solve each mirror independently, then compare image scale and whether a real image fits the entered screen limit.
| Scenario / comparison | Input or type | Signed distance / scale | Current result | Decision state |
|---|
DETAILED CALCULATION PROCESS
Formula, units, default substitution, and reconciliation
1. Governing relation
For j in {A,B}: dij = fj do/(do - fj), mj = -dij/do, hij = mj ho; feasiblej = (dij > 0 and dij <= Lscreen)
Assign a focal sign for each mirror, solve the two mirror equations separately, classify each signed result, then compare absolute scale and screen feasibility on the shared object and layout basis.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| do | Shared real-object distance | cm | 75 cm |
| ho | Shared upright object height | cm | 6 cm |
| fA, fB | Signed scenario focal lengths | cm | +25 cm; -25 cm |
| diA, diB | Signed scenario image distances | cm | Solved separately |
| mA, mB | Signed scenario magnifications | 1 | -di/do |
| Lscreen | Maximum allowed real-image distance | cm | 120 cm |
3. Unit and sign normalization
- All object, focal, image, and screen distances use centimetres.
- Each mirror-type control assigns its own focal sign; both entered magnitudes stay positive.
- Absolute scale ratio compares |mA| with |mB|, while the signed values remain available for orientation.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Five steps from measured inputs to a defensible result
- Enter one real-object distance and height that both candidate mirrors will share.
- Set the farthest usable screen location measured from each mirror vertex.
- Choose mirror type and positive focal magnitude independently for scenario A and B.
- Read signed image positions and orientations before considering the scale ratio.
- Use screen feasibility only for positive di; retain packaging, aperture, and brightness constraints separately.
MIRROR PHYSICS FOUNDATIONS
Concepts that control this specific model
- A controlled comparison shares the object basis
- Changing the object between scenarios would mix mirror choice with setup change.
- Each focal sign is independent
- Two mirrors with the same focal magnitude can produce opposite-sign image locations if one is concave and one convex.
- Only real images reach a screen
- A virtual image behind a mirror can be seen by an observer but not intercepted at that signed location.
- Screen limit is a packaging constraint
- It does not alter the optical equation; it classifies an already-solved positive image distance.
- Scale ratio discards orientation on purpose
- Absolute magnification answers which image is larger; signed magnification separately records upright or inverted.
DEEP ANALYSIS 1
Feasibility follows physics, then layout
The calculator first asks whether di is positive. Only then does it compare di with the available screen distance, preventing a negative virtual distance from passing a naive numerical limit.
DEEP ANALYSIS 2
Same focal magnitude does not mean same role
A +25 cm concave mirror can form a real inverted image for a distant object; a -25 cm convex mirror gives a reduced upright virtual image.
DEEP ANALYSIS 3
A winner needs more than one metric
A larger or screen-feasible image may still be too dim, aberrated, narrow in field, expensive, or mechanically incompatible. The comparison deliberately reports but does not invent those criteria.
RESULT INTERPRETATION
What the current output does and does not decide
A positive scenario distance within the limit identifies a first-order screen location. A negative distance means the scenario is virtual regardless of its absolute numeric size.
Absolute scale ratio above one means A has the larger image magnitude; consult signed mA and mB in the ledger for orientation.
REAL USE CASES
Two decisions with different boundary conditions
Two concave candidates under a short enclosure
A shorter-focal mirror may fit a 40 cm screen envelope while a longer-focal mirror produces a real image beyond it. Both are optically valid, but only one meets that packaging constraint.
EVIDENCE AND DATA QUALITY
What to retain with the exported result
Retain object and screen-limit measurement origins, both mirror identifiers and focal tolerances, sign convention, aperture used, predicted screen states, and observed image orientation for each trial.
LIMITS AND EXCLUSIONS
Where this physical model stops
- Compares only paraxial spherical-mirror image geometry.
- Assumes both scenarios use the same positive real-object distance and height.
- Screen feasibility ignores screen size, tilt, depth, and mechanical clearance.
- Does not compare brightness, reflectance, field of view, aberration, wavelength, cost, or durability.
- A scenario at its concave focal point is rejected because its image is not finite.
TERMS USED HERE
Six terms that keep the calculation unambiguous
- Controlled basis
- Inputs deliberately held identical across alternatives.
- Scenario
- One mirror type and focal-length choice solved independently.
- Screen feasibility
- Real positive image distance that also falls within the entered layout limit.
- Signed magnification
- Scale with orientation retained in the sign.
- Absolute scale ratio
- Ratio of image-size magnitudes with orientation removed.
- Packaging constraint
- Physical layout limit applied after the optical solution.
RELIABLE SOURCES
References supporting the equation and units
FREQUENTLY ASKED QUESTIONS
Questions specific to this calculation
Why is the object distance shared?
It isolates the effect of mirror choice; otherwise differences could come from moving the object.
Can scenario A and B use different mirror types?
Yes. That is a central use case, and each choice assigns its own focal sign.
Why is a virtual image never screen-feasible?
Its rays do not actually converge behind the mirror, so a screen there does not receive the image.
Can both scenarios be screen-feasible?
Yes, if both produce positive image distances no greater than the entered limit.
What if absolute scale ratio is less than one?
Scenario A produces the smaller image magnitude; signed magnifications still determine each orientation.
Does this choose the better mirror automatically?
No. It resolves image geometry and one screen limit; other optical, mechanical, safety, and cost criteria remain external.
IMPORTANT BOUNDARY
Use the result as analysis, not certification
This comparison is a first-order paraxial decision aid, not a complete optical trade study, tolerance analysis, or equipment certification.