If image and object distance for a spherical refracting surface—in addition to satisfying Eq. (2-19)—also satisfy the relation 1/s′ = (1/s)+(1/R), show that
a. s′=−(n1/n2)s, and
b. a(Q) for spherical aberration in Eq. (20-18) vanishes.
c. Show that a(Q) also vanishes for s′= R and for rays intersecting with the spherical surface vertex. Such image points arc called aplanatic points.
d. Find the aplanatic points for a spherical surface of +8 cm separating two media of refractive indices 1.36 and 1.70, respectively.
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