Waves, sound & light · Topic 13 of 17

Optics: Mirrors & Lenses

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Physics · optics

Lenses and mirrors form images; real images are inverted and can be projected, while virtual images are upright and cannot.

01 · Focal pointFocal point: where parallel rays meet

02 · Real vs virtualReal = can be projected; virtual = cannot

03 · Converge vs divergeConvex lens + concave mirror converge

Focal point: where parallel rays meet; focal length f = its distance must know

Concave mirror, object beyond f: real, inverted image

Concave mirror, object inside f: virtual, upright, enlarged

Convex mirror: always virtual, upright, smaller (security mirror)

Convex lens, object beyond f: real, inverted image on far side

Convex lens, object inside f: virtual, upright, enlarged (magnifier)

Concave lens: always virtual, upright, smaller

Plane mirror: virtual, upright, same size, same distance behind

1/dₒ + 1/dᵢ = 1/f (lenses and mirrors, same units)

m = hᵢ/hₒ = −dᵢ/dₒ; negative m = inverted, size > 1 = enlarged

Real images are inverted; virtual images are upright must know

Signs: f + converging, − diverging; dᵢ + real, − virtual

f = 15 cm, dₒ = 20 cm → dᵢ = +60 cm, m = −3 (real, inverted)

f = 12 cm, dₒ = 4 cm → dᵢ = −6 cm, m = +1.5 (virtual, upright)

Real image: rays really cross, can be projected; virtual: cannot must know

Converge: convex lens, concave mirror; diverge: concave lens, convex mirror must know

Commonly confused

	Real image	Virtual image
Light rays	Actually cross at the image	Only appear to come from it
On a screen?	Yes, can be projected	No
Orientation	Inverted	Upright
Image distance dᵢ	Positive	Negative
Made by	Convex lens or concave mirror, object beyond f	Plane or convex mirror, concave lens, or object inside f

Trap: a concave lens diverges, but a concave mirror converges

Show 4 more facts

Spherical mirror: f = R/2 (half the radius of curvature)

Lens power P = 1/f (f in m), unit diopter (D)

Ray tracing: center ray goes straight; parallel ray → focal point

f = −20 cm, dₒ = 20 cm → dᵢ = −10 cm, m = +0.5 (virtual, smaller)

Pearl

A concave mirror and a convex lens both gather light; a concave lens and a convex mirror both spread it.

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