Thin Lenses — Question 3

Question 3

Unequal lens curvatures combine through their signed reciprocal radii

A thin glass lens in air has index n=1.60. For left-to-right propagation, its radii are R1=+24 cm and R2=-40 cm, positive when a surface center lies to the right. Use $1/f=(n-1)(1/R_1-1/R_2)$.

1. Find focal length and optical power in inverse meters.

2. Flip the lens end for end and show whether its thin-lens focal length changes.

Question 3 - Solution

Unequal lens curvatures combine through their signed reciprocal radii

(a) Method and calculation

$$1/f=0.60(1/24+1/40)=0.0400\,\mathrm{cm^{-1}}.$$$$\boxed{f=25.0\,\mathrm{cm}=0.250\,\mathrm m,\quad\mathcal P=4.00\,\mathrm{m^{-1}}}.$$

(b) Interpretation and further calculation

$$R_1^\prime=+40\,\mathrm{cm},\quad R_2^\prime=-24\,\mathrm{cm}.$$$$1/f^\prime=0.60(1/40+1/24)=1/f\Rightarrow\boxed{f^\prime=f}.$$

Physical check

Reversing a thin lens in the same medium leaves its paraxial power unchanged, though aberrations can depend on orientation.