Optical Instruments — Question 3

Question 3

Accommodation changes optical power while the retinal plane stays fixed

Model an eye as a thin lens in air with a fixed lens-to-retina distance of 17 mm. Ignore the internal refractive-index structure. The lens changes power to focus either an object at infinity or one 25 cm away.

1. Find the optical power for infinity focus.

2. Find the power for the near object and the required change in power.

Question 3 - Solution

Accommodation changes optical power while the retinal plane stays fixed

(a) Method and calculation

$$p\to\infty:\quad\mathcal P_\infty=1/q=1/(0.017\,\mathrm m).$$$$\boxed{\mathcal P_\infty=58.8235\,\mathrm{m^{-1}}}.$$

(b) Interpretation and further calculation

$$\mathcal P_{\mathrm{near}}=1/(0.25)+1/(0.017)=\boxed{62.8235\,\mathrm{m^{-1}}}.$$$$\boxed{\Delta\mathcal P=4.00\,\mathrm{m^{-1}}}.$$

Physical check

The increment is exactly the added object vergence in this idealized model; these values are not a clinical eye model.