Optical instrument problems and solar technology

In a camera problem use Γ = h/H and d = F(1 + Γ)/Γ, with distances in metres. For a magnifier K = D₀/F, D₀ = 25 cm = 0.25 m. For a microscope K ≈ l·D₀/(F₁F₂) (all in the same unit, usually centimetres). In a spectacles problem the unaided eye sees best at a distance a, while with spectacles an object must be seen at the normal distance d₀ = 25 cm. The spectacle lens must form a virtual image at distance a of a point at distance d₀ from it, so D = 1/d₀ – 1/a. For short-sightedness a < d₀ and D < 0 (concave lens); for long-sightedness a > d₀ and D > 0 (convex lens). Finally check the sign of D against the type of spectacles.