By Manneville P.

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P and Q are conjugate points. Axial distances z1 , z2 are measured from the focal planes F1, F2 shows that the principal planes are conjugate planes of unit magnification: if the object point is in one, the image point is in the other and at the same height. By substituting z1 ¼ 0, we obtain z2 ¼ 1, infinite magnification, and each focal plane has a conjugate plane at infinity. The constants f1 and f2 are the principal focal lengths of the system. 9). 9). 20) respectively for a thin lens, a single refractive surface and a spherical mirror.

10) for v : v ¼ fu=ðf þ uÞ ¼ 0:05ðÀ0:7Þ=ð0:05 À 0:7Þ ¼ 0:054 m ¼ 54 mm. We have already related the focal length of the lens to the refractive index n and the radius of curvature r of the two equally curved surfaces. 4) gives the focal length 1 1 1 ¼ ðn À 1Þ À f r1 r2 ð2:11Þ where the subscripts refer to the first and second interfaces crossed by the incident light. 3(a), r1 > 0 and r2 < 0; hence both surfaces add to the positive value of the power. 3(b), the signs of r1 ; r2 are the opposite, and both contribute to a negative power.

3 Or, more rarely, a maximum. 3 Convex (a) and concave (b) lenses changing the curvature of a wavefront. 8), the curvatures are evaluated on wavefronts immediately adjacent to the lens We now introduce the term vergence for the curvature of a wavefront, using a definition which applies generally to refraction and reflection at curved surfaces. The vergence V of a wavefront emanating from (or converging to) an object (or image point) at signed distance L in a medium with refractive index n is defined as V ¼ n=L; the sign of L is chosen so that vergence is positive for a converging wavefront and negative for a diverging wavefront.