Note 60 — PART SECOND. NOTES ON THE ILLUMINATION OF LIGHTHOUSES, WITH SHORT NOTICES OF THEIR EARLY HISTORY. (continued 2)

This will be easily seen by examining the annexed figure (64), in which Q q represents the lens. A its centre, F the principal focus, b F and b′ F the radius of the flame; then is the angle b A b′ equal to the maximum divergence of the lens. Sin b AF = b FAF = sin b′ AF = Rad. of flameFocal distance; and twice b AF = the whole divergence at A. Then for the divergence at the margin of the lens, or at any other point, we have, FQ = √AQ² + AF² and Q x = √QF² + F x²; and for any angle at Q, we have sin FQ x = F xFQ.

Fig. 64.