WAV-10

Thin-lens equation

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

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WavesThin lens

Governing equation

\dfrac1f=\dfrac1u+\dfrac1v

where

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

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