WAV-10

Thin-lens equation

1/f = 1/u + 1/v. Gaussian sign convention.

Reading speed

WavesThin lens

Governing equation

\dfrac1f=\dfrac1u+\dfrac1v

$u \in \left[5, 200\right]$

where

u: Object distance (cm)
f: Focal length (cm)
v: Image distance (cm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\dfrac1f=\dfrac1u+\dfrac1v

$u \in \left[5, 200\right]$

$u = 5$ $v = -10$

Along the curve

②

Domain of the variable — blue

u_{\min} = 5,\quad u_{\max} = 200

$u \in \left[5, 200\right]$

$u = 5$ $u = 5$

Along the curve

③

Response curve — green

\dfrac1f=\dfrac1u+\dfrac1v

$u \in \left[5, 200\right]$

$u = 5$ $v = -10$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}u}

$u \in \left[5, 200\right]$

$u = 6.226$ $v^{\prime} = -7.852$

Along the curve

Lecture brief

Historical brief

d’Alembert’s wave equation, Snell, the thin-lens maker, Doppler and Bragg interference are the classical optics-and-sound toolkit. The lab is propagation, image and shift. This sheet (WAV-10 — Thin-lens equation) is the form associated with Thin lens. Working symbols: $u$ , $f$ $\rightarrow$ $v$ . Paraxial rays. Magnification m = −v/u.

Purpose

Purpose: compute

v

from

u

f

in Waves & optics via

\dfrac1f=\dfrac1u+\dfrac1v

1/f = 1/u + 1/v. Gaussian sign convention. Use it when a real waves & optics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

u = 30.000\,\mathrm{cm}

f = 10.000\,\mathrm{cm}

, the governing relation

\dfrac1f=\dfrac1u+\dfrac1v

yields

v = 15.00\,\mathrm{cm}

. A lens, an object arrow, an inverted image. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Object distance u30 cmFocal length f10 cm

Outputs

Image distance v15.00 cm

Reading speed

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Narration of this film

A lens, an object arrow, an inverted image.

Paraxial rays. Magnification m = −v/u.

Reading speed

Watch on YouTube