The following thin lenses are made of glass with an index of refraction of 1.5. Make a sketch of each lens, and find its focal length in air:

(a) Double convex, r₁ = 10 cm and r₂ = –21 cm;

(b) Plano–convex, r₁ = ∞ and r₂ = –10 cm;

(c) Double concave, r₁ = –10 cm and r₂ = +10 cm;

(d) Plano–concave, r₁ = ∞ and r₂ = +20 cm.