All Problems

Diffraction of Light

Problem 5.148

Determine the minimum multiplication of a telescope with diameter of objective D=5.0 cmD=5.0 \mathrm{~cm} with which the resolving power of the objective is totally employed if the diameter of the eye's pupil is d0=4.0 mmd_{0}=4.0 \mathrm{~mm}.

Reveal Answer
5.148. Suppose Δψ\Delta \psi and Δψ′\Delta \psi^{\prime} are the minimum angular separations resolved by the telescope's objective and the eye respectively (Δψ=1.22λ/D,Δψ′=1.22λ/d0).\left(\Delta \psi=1.22 \lambda / D, \Delta \psi^{\prime}=1.22 \lambda / d_{0}\right) . Then the sought magnification of the telescope is Γmin⁡=Δψ′/Δψ=D/d0=13\Gamma_{\min }=\Delta \psi^{\prime} / \Delta \psi=D / d_{0}=13
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