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

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Why it behaves this way

Explanation

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.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

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.

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View plans

Frozen valuesUsing frozen 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?

Make a prediction before you reveal the next step.

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

Check your reasoning against the live bench.

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?

Use the live bench to test the result before moving on.

Accessibility

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 this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Build into lensesOptics

Mirrors

Explanation

Step through the frozen example

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 this idea moving

Lens Imaging

Refraction / Snell's Law

Wave Interference