OpticsIntro

Concept module

Mirrors

Use plane, concave, and convex mirrors to track equal-angle reflection, signed image distance, and magnification on the same live ray diagram.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Mirrors

Drag the object arrow or use the controls. The mirror diagram, equal-angle cue, and response graphs stay on the same geometry.

Graphs

Switch graph views without breaking the live stage and time link.

Object to image map

Shows how the signed image distance responds when you move the object while keeping the same mirror type and focal-length magnitude.

object distance d_o (m): 0.35 to 4signed image distance d_i (m): -4.4 to 4.4

Virtual branchReal branch

Hover or scrub to link the graph back to the stage.object distance d_o (m) / signed image distance d_i (m)

Controls

Adjust the physical parameters and watch the motion respond.

Curved mirrorTurn this off for a plane mirror. Leave it on for concave or convex mirror behavior.Concave mirrorWith Curved mirror on, turn this off to switch to a convex mirror with the same focal-length magnitude.

Focal-length magnitude

f

0.8 m

Controls where $F$ and $C$ sit for the curved-mirror cases.

Object distance

d_{o}

2.4 m

Moves the object along the principal axis.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

Object height

h_{o}

1 m

Changes the object size so the image-height comparison stays visible.

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

Graph readingPrompt 1 of 2

Notice that the mirror graphs are object-distance based, not time based: hovering a point previews a different geometry immediately, not a later moment.

Try this

Hover the image map and watch the object jump to the matching position while the reflected-ray geometry updates in one step.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

f

Focal length

0.8 m

Sets how strongly a curved mirror redirects the principal rays. In this module, concave uses positive $f$ and convex uses negative $f$.

Graph: Object to image mapGraph: MagnificationOverlay: F and C markersOverlay: Principal rays

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use the live prompt to connect equal-angle reflection, the ray construction, and the graph branch that the current mirror lives on.

Graph readingPrompt 1 of 2

Graph: Object to image map

Notice that the mirror graphs are object-distance based, not time based: hovering a point previews a different geometry immediately, not a later moment.

Try this

Hover the image map and watch the object jump to the matching position while the reflected-ray geometry updates in one step.

Why it matters

It keeps the graph honest: you are comparing families of setups, not stepping through time.

Graph: Object to image mapOverlay: Principal rays

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

3 visible

Overlay focus

Equal-angle cue

Shows the normal at the pole and reminds you that the incident and reflected angles match there.

What to notice

The pole ray always reflects symmetrically about the principal axis.

Why it matters

It keeps the law of reflection visible instead of turning the ray diagram into a memorized sketch.

Control: Curved mirrorControl: Object distanceEquation

d_{o}

Challenge mode

Use the real mirror controls and graphs to hit image targets. The checks read the live signed distances and magnification instead of a separate puzzle state.

0/2 solved

TargetCore

2 of 4 checks

Real-image target

Starting from the concave real-image preset, tune the setup until the image distance lands between 1.0 and 1.2 m and the magnification lands between -1.4 and -1.1.

Graph-linkedGuided start2 hints

Suggested start

Use the image map and the reflected-ray intersection together.

Matched

Open the object-image map.

Object to image map

Matched

Keep the principal rays visible.

Pending

Make

d_{i}

land between 1.0 and 1.2 m.

1.2 m

Pending

Keep magnification between -1.4 and -1.1.

-0.5

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

The concave mirror uses signed focal length 0.8 m. An object at 2.4 m with height 1 m forms a inverted, smaller real image at 1.2 m, with magnification -0.5.

Equation detailsDeeper interpretation, notes, and worked variable context.

Law of reflection

At the reflecting surface, the incident and reflected rays make equal angles with the normal.

θ_{i} = θ_{r}

Mirror equation

Relates signed focal length, object distance, and image distance for the paraxial mirror cases shown here.

\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}

For a plane mirror, the focal length is effectively infinite, so the relation reduces to $d_i = -d_o$.

f

Focal length 0.8 m

d_{o}

Object distance 2.4 m

Magnification

Gives the size ratio and the orientation sign of the image.

m = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}

d_{o}

Object distance 2.4 m

h_{o}

Object height 1 m

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Short explanation

What the system is doing

Mirror imaging starts from one compact rule: the angle of incidence equals the angle of reflection. Once that geometric rule is applied consistently, the reflected rays either meet in front of the mirror to make a real image or only appear to meet behind the mirror to make a virtual image.

This module keeps the stage deliberately bounded. You switch between plane, concave, and convex mirrors, then change focal-length magnitude, object distance, and object height. The ray diagram, signed mirror equation, magnification, worked examples, prediction mode, compare mode, and response graphs all stay tied to that same mirror geometry.

Key ideas

01A plane mirror keeps the image virtual, upright, and the same size, with the image the same distance behind the mirror as the object is in front.

02A concave mirror can make a real inverted image in front of the mirror when the object is outside the focal length, but it flips to a virtual upright image behind the mirror when the object moves inside the focal length.

03A convex mirror always makes a virtual upright reduced image, and the signed mirror equation plus magnification explain that behavior without needing a separate rulebook.

Live worked example

Solve the exact state on screen.

Solve the current mirror, not a detached worksheet. The substitutions follow the live controls, and the same signed values stay visible on the stage and in the graphs.

Live valuesFollowing current parameters

For the current concave mirror, what signed image distance follows from the mirror equation?

f

Signed focal length

0.8 m

d_{o}

Object distance

2.4 m

1. Start from the mirror relation

Use

\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}

2. Rearrange for the signed image distance

\frac{1}{d _{i}} = \frac{1}{f} - \frac{1}{d _{o}} = 1.25 - 0.42 = 0.83

3. Invert the result

d_{i} = 1.2 m

Signed image distance

d_{i} = 1.2 m

A positive image distance means the reflected rays really cross in front of the mirror, so the image can be caught on a screen.

Common misconception

A virtual image is fake because no light actually goes there, so it does not count as an image.

A virtual image is still a real geometric result. The reflected rays do not cross there physically, but their backward extensions do meet there consistently.

That is why your eye still receives the reflected light in a way that makes the image appear at a definite location behind the mirror.

Mini challenge

A concave mirror currently has the object outside the focal point. Before you drag the object inward past

F

, what should happen to the image type and orientation?

Prediction prompt

Decide when the real image disappears and what replaces it after the object crosses inside the focal point.

Check your reasoning

The real inverted image runs farther away as the object approaches

F

, then flips to a virtual upright image behind the mirror once the object crosses inside

F

Outside

F

, the reflected rays still meet in front of the mirror. At the focal limit the image distance blows up, and inside

F

the reflected rays separate so only their backward extensions meet behind the mirror.

Quick test

Reasoning

Question 1 of 4

Use the ray behavior, the sign of

d_{i}

, and the sign of

m

together. The goal is to reason from the live mirror model, not to recite isolated slogans.

Which statement best describes the image in a plane mirror?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a mirror at the center of the principal axis, an object arrow on the left, and an image arrow that moves according to the selected mirror type. Depending on the setup, the image arrow appears in front of the mirror as a real inverted image or behind the mirror as a virtual upright image.

Optional overlays show the equal-angle cue at the pole, the focal markers for curved mirrors, the principal rays, and the distance-and-height guide used in magnification.

Graph summary

The object-image graph plots signed image distance against object distance for the current mirror family and focal-length magnitude.

The magnification graph plots $m$ against object distance, so the sign and magnitude of the image scaling are visible without leaving the ray diagram.

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Build into lensesOptics

Mirrors

See each variable before you move it.

Equal-angle cue

Real-image target

What the system is doing

Solve the exact state on screen.

For the current concave mirror, what signed image distance follows from the mirror equation?

Which statement best describes the image in a plane mirror?

Keep moving through the concept map.

Lens Imaging

Refraction / Snell's Law

Wave Interference