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Chapter 9 · Physics

Light — Reflection and Refraction

Every ray diagram in this chapter is drawn from the mirror and lens equations in real time. Move the object and the image position, size, nature and magnification are recomputed from the actual physics — nothing is pre-drawn.

Optical Bench — Mirrors & Lenses

Everything below is solved live from the mirror/lens equation. Nothing is pre-drawn.

FCObjectImage
Formula
1/v + 1/u = 1/f
u
-30.0 cm
f
-20.0 cm
v
-60.00 cm
m = h′/h
-2.00
h′
-12.00 cm
Nature
Real, inverted
Size
Enlarged

Formula sheet

Mirror formula

1/v + 1/u = 1/f

Relates image distance v, object distance u and focal length f.

All distances measured from the pole, with the sign convention.

Magnification (mirror)

m = −v/u = h′/h

Negative m means a real, inverted image.

Focal length

f = R/2

Focal length is half the radius of curvature.

Lens formula

1/v − 1/u = 1/f

Note the minus sign — this is what differs from the mirror formula.

Magnification (lens)

m = v/u = h′/h

Positive m means an erect, virtual image.

Power of a lens

P = 1/f (f in metres), unit dioptre (D)

Convex lens has positive power, concave negative.

Refractive index

n = c/v = sin i / sin r

Snell's law; n₂₁ = n₂/n₁.