Classify mirror images before placing a screen
A spherical mirror is described here by a paraxial focal length, meaning rays remain close enough to the axis that the simplified imaging equation applies. A concave converging mirror has positive f and a convex diverging mirror negative f. The real object distance o is positive in front of the mirror. A positive image distance i lies in front of the mirror, while negative i locates a virtual image behind it.
Learning outcome: Compare objects inside, at and beyond the positive focal distance, then switch to negative f. Sketch two principal rays before consulting the image location. State which images can be screen-focused and why the focal case is not assigned a large arbitrary number.
Starting recap
Use normal-based angles, signed conjugate distances and explicit optical-path/reflection phases. Separate geometric direction, amplitude and energy; preserve focal and critical boundaries.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
For f=+10 cm and o=15 cm, i=30 cm in front and m=−2: a 1 cm object has an inverted 2 cm image. At o=5 cm, i=−10 cm and m=+2, a virtual upright enlarged image. A convex mirror with f=−10 cm and o=10 cm gives i=−5 cm,m=.5.
Open the experimentPredict
For a concave mirror with f=10 cm and object distance15 cm, the image is:
Experiment
Compare objects inside, at and beyond the positive focal distance, then switch to negative f. Sketch two principal rays before consulting the image location. State which images can be screen-focused and why the focal case is not assigned a large arbitrary number.
Keep mirror focal and virtual-image branches distinct
Worked teaching model · synthetic values · Paraxial spherical mirror with focal length f=10b cm. Real object height1 cm in front, distance o>0. Positive image distance is in front of mirror, negative behind; m=−i/o. At o=f rays are parallel and no finite image distance/magnification is reported.
Reset keeps your prediction, captures and practice history.
Paraxial mirror object and image locations
Spatial axes use the same pixels per physical unit, preserving geometry. 1: object before optical surface (solid).2: real image (dashed).3: optical surface (dotted).4: optical axis extent (dotted). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Paraxial mirror object and image locations
object before optical surface
| axis coordinate (cm) | height (cm) |
|---|---|
| -15 | 0 |
| -15 | 1 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
real image
| axis coordinate (cm) | height (cm) |
|---|---|
| -30 | 0 |
| -30 | -2 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
optical surface
| axis coordinate (cm) | height (cm) |
|---|---|
| 0 | -2 |
| 0 | 2 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
optical axis extent
| axis coordinate (cm) | height (cm) |
|---|---|
| -30 | 0 |
| 30 | 0 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
| Quantity | Value | Unit |
|---|---|---|
| Signed focal length | 10 | cm |
| Object distance | 15 | cm |
| Object at focal distance | 0 | flag |
| Optical power from focal length | 10 | m⁻¹ |
| Signed image distance | 30 | cm |
| Transverse magnification | -2 | ratio |
| Image height | -2 | cm |
| Real image branch | 1 | flag |
| Reciprocal equation residual | 6.93889e-18 | cm⁻¹ |
The model forms a real inverted image; a screen would need the calculated image plane.
Use 1/f=1/o+1/i with a positive real object distance. A converging/concave element has positive f, a diverging/convex element negative f, and m=−i/o. Mirror positive image distance lies back in front of the mirror, whereas lens positive image distance lies after the lens. The location diagram marks objects and images, not a full ray trace. Paraxial approximation excludes strong off-axis rays, spherical/chromatic aberration and aperture clipping.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
The model forms a real inverted image; a screen would need the calculated image plane.
Use 1/f=1/o+1/i with a positive real object distance. A converging/concave element has positive f, a diverging/convex element negative f, and m=−i/o. Mirror positive image distance lies back in front of the mirror, whereas lens positive image distance lies after the lens. The location diagram marks objects and images, not a full ray trace. Paraxial approximation excludes strong off-axis rays, spherical/chromatic aberration and aperture clipping.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
Understand
Apply
Public practice checks a specific claim. It does not establish independent mastery.
Which independent observation would reject the approximation, sign convention or calibration premise rather than merely refit it?
Continue
Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.
Skipping retains experiments and awards no mastery.
Save a science backup or import one
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
Complete file sets and course backups
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
Science storage: loading. No account or remote computation is required.