Thin Lenses — Question 6

Question 6

The back focus of a separated lens pair differs from its effective focal length

Use the thin-lens relations $1/p+1/q=1/f$ and $m=-q/p$ in one surrounding medium. Distances p and q are positive for real objects and real images; f is positive for a converging lens. A parallel beam meets lens 1 with f1=10 cm, then lens 2 with f2=-20 cm located d=5 cm farther right. The effective power is supplied as $1/F=1/f_1+1/f_2-d/(f_1f_2)$.

1. Use successive imaging to find the final distance from lens 2.

2. Calculate effective focal length F and explain why it differs from that distance.

Question 6 - Solution

The back focus of a separated lens pair differs from its effective focal length

(a) Method and calculation

$$q_1=f_1=10\,\mathrm{cm},\quad p_2=d-q_1=\boxed{-5\,\mathrm{cm}}.$$$$1/q_2=-1/20-1/(-5)=3/20\Rightarrow\boxed{q_2=20/3\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$1/F=1/10-1/20-5/[10(-20)]=3/40\Rightarrow\boxed{F=40/3\,\mathrm{cm}}.$$$$\boxed{q_2=(1-d/f_1)F=F/2}.$$

Physical check

Effective focal length is referred to a principal plane of the compound system, whereas q2 is measured from the physical second lens.