{Distance between lens and screen (in feet) × Diameter of slide (in inches)} / Diameter of picture (in feet) = Focus of lens in inches;
or, if we know the focus of the lens but want to know how far from the screen we must go to produce a given-sized picture, the formula will be:
{Diameter of picture (in feet) × Focus of lens (in inches)} / Diameter of slide (in inches) = Distance required (in feet).
It is handy for the lanternist to remember that, dealing with a standard 3-inch slide, a 6-inch lens will always give a picture whose diameter is one-half the distance from lens to screen, a 12-inch lens half this again or one-quarter, and a 9-inch lens half-way between the two.
Bearing these simple figures in mind, the approximate distance can usually be guessed sufficiently near for the first trial, and then the lantern shifted a little nearer or the reverse as required.
The following table may, however, be useful, as showing readily the magnification produced at different distances by lenses of given foci:
| Disc wanted | Focus 4½ in. | Focus 6 in. | Focus 8 in. | Focus 10 in. | Focus 12 in. | Focus 15 in. | Focus 18 in. |
| feet. | ft. in. | ft. in. | ft. in. | ft. in. | ft. in. | ft. in. | ft. in. |
| 9 | 13 6 | 18 0 | 24 0 | 30 0 | 36 0 | 45 0 | 54 0 |
| 12 | 18 0 | 24 0 | 32 0 | 40 0 | 48 0 | 60 0 | 72 0 |
| 15 | 22 6 | 30 0 | 40 0 | 50 0 | 60 0 | 75 0 | 90 0 |
| 18 | 27 0 | 36 0 | 48 0 | 60 0 | 72 0 | 90 0 | 108 0 |
| 20 | 30 0 | 40 0 | 53 4 | 66 8 | 80 0 | 100 0 | 120 0 |
| 25 | 37 6 | 50 0 | 66 8 | 83 4 | 100 0 | 125 0 | 150 0 |
| 30 | 45 0 | 60 0 | 80 0 | 100 0 | 120 0 | 150 0 | 180 0 |
The Diameter of the Objective.—The diameter of the objective must depend to a certain extent upon its focus in the case of a double combination such as a Petzval. These lenses consist, as has already been said, of two achromatic components some distance apart, and for technical considerations, which need not be discussed here, the distance between these components is usually about two-thirds of the focal length. This is not a universal rule, as the lenses of different makers vary a good deal; but it is generally a fact
that the longer the focus of the lens the greater is usually the separation between the two lens systems.