Note 45 — PART SECOND. NOTES ON THE ILLUMINATION OF LIGHTHOUSES, WITH SHORT NOTICES OF THEIR EARLY HISTORY.
Reading edition
The truth of this equation may be easily ascertained as follows (See fig. 27):—Let AP be the mirror, F its principal focus, and PH the line of reflection of the ray FP; then an object at I will be reflected at P to the conjugate focus O, where the screen is supposed to be placed. But by construction, FPI = HPO = POF, and the angle at F being common, the triangle FPI is similar to FPO, and hence FO ∶ PF ∷ PF ∶ FI, and FI = PF²FO; and substituting the letters in the text, we get d ∶ r ∷ r ∶ b, and b = r²d.
Fig. 27.
