Sign and Side Audits

Signed Height Audit

orientation from magnification

Signed magnification turns a positive object height into an inverted or upright image height. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Magnification is a signed height contract

Use object height 4 metres. The signed image height is object height multiplied by magnification.

himage=mhobjecth_{\text{image}} = m h_{\text{object}}
Signed height auditThe checked lens case draws the signed image height.FFlensobjectimage

The same object height can draw different image heights

Hold object height fixed and change the object placement. The same height can produce a smaller inverted image, a taller inverted image, or an upright virtual image.

uvmhimage30 m15 m−12−2 m15 m30 m−2−8 m5 m−10 m28 m\begin{array}{c|c|c|c}u&v&m&h_{\text{image}}\\30\ \text{m}&15\ \text{m}&\tfrac{-1}{2}&-2\ \text{m}\\15\ \text{m}&30\ \text{m}&-2&-8\ \text{m}\\5\ \text{m}&-10\ \text{m}&2&8\ \text{m}\\\end{array}
Signed height auditThe middle row is the checked tall inverted image.FFlensobjectimage

Read orientation from the sign of height

A negative signed image height means the drawn image is inverted relative to the object. A positive signed image height means the drawn image is upright.

himage<0⇒inverted,himage>0⇒uprighth_{\text{image}}<0\Rightarrow \text{inverted},\qquad h_{\text{image}}>0\Rightarrow \text{upright}
Signed height auditThe positive-height row is the checked virtual diagram.FFlensobjectimage