Thin Lenses — Question 5

Question 5

Contact lenses add optical powers rather than focal lengths

Two thin lenses in air are placed in contact. Their powers are +10 inverse meters and -4 inverse meters. The combination views a real object 0.50 m away. Treat the separation as zero.

1. Find the equivalent focal length and image distance.

2. Find the power of a third contact lens that makes the complete combination afocal.

Question 5 - Solution

Contact lenses add optical powers rather than focal lengths

(a) Method and calculation

$$\mathcal P=\mathcal P_1+\mathcal P_2=\boxed{6\,\mathrm{m^{-1}}},\quad\boxed{f=1/6\,\mathrm m}.$$$$1/q=\mathcal P-1/p=6-2=4\Rightarrow\boxed{q=0.250\,\mathrm m}.$$

(b) Interpretation and further calculation

$$\mathcal P_{\mathrm{total}}=6+\mathcal P_3=0.$$$$\boxed{\mathcal P_3=-6\,\mathrm{m^{-1}},\quad f_3=-1/6\,\mathrm m}.$$

Physical check

Afocal means parallel input remains parallel; it does not mean a finite-distance object has no outgoing divergence.