Physics · Mirrors and Lenses

Mirrors

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Lens ImagingApply signed imaging to lenses

Key takeaway

Use equal-angle reflection as the common rule behind every mirror on the page.
Read real versus virtual image type from where reflected rays meet or only appear to meet.
Use the signs of d_i and m to name image side, orientation, and size change.
Predict how plane, concave, and convex mirrors differ without memorizing separate rule lists.

Common misconception

A virtual image is not fake; it is a consistent apparent location found by extending reflected rays backward.

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

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Build into lensesMirrors and Lenses

Lens Imaging

Trace principal rays through converging and diverging lenses, connect the signed thin-lens equation to the diagram, and watch image distance and magnification respond to the same object setup.

Boundary angle ruleOptics

Refraction / Snell's Law

Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.

Contrast wave opticsWaves

Wave Interference

Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.

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Reference and support

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Equation snapshotLaw of reflection · Mirror equationShow 3 equations

Use equal-angle reflection to draw the rays, then use the mirror equation and magnification signs to name the image side, orientation, and size.

Law of reflection
$θ_{i} = θ_{r}$
At the reflecting surface, the incident and reflected rays make equal angles with the normal.
Mirror equation
$\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$
Relates signed focal length, object distance, and image distance for the current mirror.
Magnification
$m = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}$
The sign of m gives orientation, and the magnitude |m| gives the size ratio.

Why it behaves this way

Explanation

Every mirror image starts from the same rule: the angle of incidence equals the angle of reflection. If the reflected rays really meet, the image is real. If the reflected rays spread apart but their backward extensions meet, the image is virtual.

This bench keeps plane, concave, and convex mirrors on one shared geometry. As you change mirror type, focal-length magnitude, object distance, and object height, the stage, signed image distance, and magnification all update together. That lets you connect what the rays do, where the image forms, and whether it is upright or inverted without treating them as separate rules.

Worked examples

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These examples use the current mirror, object position, and object height from the live bench, so each calculation matches the ray diagram you are actually seeing.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current concave mirror, what signed image distance does the mirror equation predict, and what does the sign tell you about the image?

f

Focal length

0.8 m

d_{o}

Object distance

2.4 m

1. Start with the mirror equation

Use

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

2. Solve for the signed image distance

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

3. Interpret the sign of the result

d_{i} = 1.2 m

Signed image-distance result

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.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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 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 gives orientation and the magnitude gives the image-size scale without leaving the ray diagram.

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Concave real image preset

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