Optical Instruments — Question 6

Question 6

A magnifier held away from the eye has a smaller near-point advantage

A thin positive magnifier has f=5.0 cm and is held e=2.0 cm in front of an eye whose near-point distance is D=25 cm. Compare angular size with unaided viewing of the same object at D. Place the final virtual image at the eye near point.

1. Find the signed lens image distance and required object distance.

2. Find angular magnification and compare with relaxed viewing through the same lens.

Question 6 - Solution

A magnifier held away from the eye has a smaller near-point advantage

(a) Method and calculation

$$\boxed{q=-(D-e)=-23\,\mathrm{cm}},\quad1/p=1/f+1/(D-e).$$$$\boxed{p=\frac{f(D-e)}{f+D-e}=115/28=4.10714\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$M=\frac{h_I/D}{h/D}=m=\frac{D-e}{p}=\boxed{1+(D-e)/f=5.60}.$$$$\boxed{M_\infty=D/f=5.00}.$$

Physical check

The familiar near-point factor 1+D/f assumes the lens is at the eye; retaining e makes the geometry explicit.