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An angular readout using a reflected light ray: rotating a mirror by $\theta$ rotates the reflected light ray by $2\theta$, giving spot displacement $x\simeq 2D\theta$ at distance $D$ for small angles.

A mirage is an apparent displaced image caused by refraction through a spatially varying refractive index. Above a hot surface, low-index air near the ground can bend a light ray back upwards before it reaches the surface. An observer tracing the arriving ray backwards along its local tangent can then infer an apparent image below the turning region. This explains the appearance of a distant reflective surface without requiring reflection at the road itself.

Locating genetic markers or other features within a genome. Physical positions use DNA sequence distances, while linkage maps use genetic recombination frequencies.

Plasmid selection and confirmation separate recovering candidates from establishing what they contain. In an original idealized comparison, stipulate a susceptible recipient and a selectable marker that permits growth under the chosen condition. The intended 6000-base pair construction and an empty carrier retaining that marker can both yield biological colonies. If removal of the 1500-base pair plasmid insert followed by DNA ligation joins its two boundaries without losing other material, the empty carrier is $6000-1500=4500$ base pairs. Selection for their shared selectable marker cannot distinguish these candidates.

Use separate scientific controls for separate uncertainties. A recipient-only comparison tests background growth under selection. A known intact plasmid tests whether recipient preparation, genetic transformation and recovery can yield selected carriers. A carrier-only construction comparison tests recovery in the absence of added plasmid insert. Growth on supporting cell culture medium tests viability under that supporting condition. These are analytical comparisons for the constructed example, not a list claimed to have been performed in the 1973 plasmid construction experiment.

Recover candidate DNA, compare a complete restriction digest with the stipulated pattern, and inspect relevant joins by DNA sequencing. Each step narrows the claim: selection supports a growth phenotype; length comparison supports size and some structural features; DNA sequencing tests the letters sampled. Even a confirmed nucleotide sequence does not alone show the intended biological function. That requires an appropriate readout such as functional complementation, with its own scientific controls and recipient genetic background.