Virtual laboratory/Physics/Optics/Spherical mirrors — concave and convex

Spherical mirrors — concave and convex

What we'll do: We'll move an object in front of a concave and a convex mirror and check what image forms and where.

What you see on screen: A mirror with its axis, focal point and centre of curvature, an object-arrow and the reflected characteristic rays that form the image; a mirror-type toggle and sliders for distance and radius. Readouts: mirror type, focal length, distances x and y, magnification, plus the image type and orientation.

Spherical mirrors — concave and convex
Physics · Optics · Spherical mirrors (FIZ.3.4.3)
Type:
Object distance xx30 cm
Radius of curvature RR24 cm
A CONVEX mirror (e.g. a car's rear-view mirror) — what image does it form?
mirror
convex
focal f
-12 cm
object x
30 cm
image y
-8.6 cm
magnif.
0.29×
image
virtual, upright, reduced
🎯 Challenge: produce the required image type (pick the mirror type and position)

What just happened?

The convex mirror formed a virtual, upright and reduced image — and that is ALWAYS the case, regardless of distance. That is why a rear-view mirror shows a wide area behind the car.

Two kinds of spherical mirrors:

CONCAVE (converging): reflects rays toward the focal point. The image depends on the object position — far away it forms a real, inverted image (as in a headlight), and up close (closer than the focal point) — enlarged and upright (a makeup mirror). CONVEX (diverging): scatters rays. The image is ALWAYS virtual, upright and reduced, but it covers a wider field of view (rear-view and shop mirrors).

The mirror equation:

1f=1x+1y\frac{1}{f} = \frac{1}{x} + \frac{1}{y}
f=R2f = \frac{R}{2}

ff — focal length (positive for concave, negative for convex), xx — object distance, yy — image distance, RR — radius of curvature. Magnification:

p=∣y∣xp = \frac{|y|}{x}

Why you need this for the exam:

constructing images in mirrors and the mirror equation are typical optics problems (twins of lens problems). Trick: treat a concave mirror like a converging lens, a convex one like a diverging lens.

Remember: a concave mirror converges (image depends on position), a convex one diverges (always virtual, upright, reduced). Equation: 1/f=1/x+1/y1/f = 1/x + 1/y, f=R/2f = R/2.

Illustrative model · NexTutor Virtual laboratory

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Theory & formulas

The mirror equation

For a spherical mirror: 1f=1x+1y,f=R2\dfrac{1}{f} = \dfrac{1}{x} + \dfrac{1}{y},\qquad f = \dfrac{R}{2} The focal length ff is positive for a concave mirror and negative for a convex one.

Convex mirror

It always forms a virtual, upright and reduced image — hence its use in rear-view and shop mirrors (a wide field of view).

Concave mirror

The type of image depends on the object position: for x>fx>f the image is real and inverted, for x<fx<f it is virtual, upright and enlarged (a makeup mirror).

Symbols: ff — focal length, RR — radius of curvature, xx — object distance, yy — image distance.

Frequently asked questions

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What is the spherical mirror equation?

1/f = 1/x + 1/y, where f = R/2 (f positive for a concave mirror, negative for a convex one).

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What image does a convex mirror form?

Always virtual, upright and reduced — that is why they are used as rear-view and shop mirrors.

›

When does a concave mirror form an enlarged, upright image?

When the object is closer than the focal point (x < f) — it then acts as a magnifying mirror.

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