Optical Instruments — Question 4

Question 4

A corrective lens for a finite far point creates a virtual distant-object image

In an ideal paraxial model, an unaccommodated eye focuses objects at a far point 0.80 m in front of the eye. A corrective thin lens must make parallel incoming rays appear to originate at that point.

1. Find the lens power if placed at the eye plane.

2. Find the required power if the lens instead stands 0.020 m in front of the eye, keeping the same virtual image location relative to the eye.

Question 4 - Solution

A corrective lens for a finite far point creates a virtual distant-object image

(a) Method and calculation

$$p\to\infty,\ q=-0.80\,\mathrm m\Rightarrow\boxed{f=-0.80\,\mathrm m}.$$$$\boxed{\mathcal P=-1.25\,\mathrm{m^{-1}}}.$$

(b) Interpretation and further calculation

$$|q_{\mathrm{lens}}|=0.80-0.020=0.780\,\mathrm m\Rightarrow\boxed{q_{\mathrm{lens}}=-0.780\,\mathrm m}.$$$$\boxed{\mathcal P_{\mathrm{offset}}=-1/0.780=-1.28205\,\mathrm{m^{-1}}}.$$

Physical check

This sign and distance exercise uses a specified ideal far point; the virtual image distance is measured from the corrective lens, not from the eye.