Hyperopia Corrected: The Converging Lens at Work

1 · Predict

A hyperopic eye's converging corrective lens (f = 33 cm here) is meant to make a close object appear to be at the eye's (pushed-out) near point instead. As the true object gets closer to the lens's own focal length, what happens to the image distance?

• It grows rapidly in magnitude — as the true object distance approaches the lens's focal length, the virtual image distance changes dramatically.
• The image distance stays roughly constant.
• The image distance shrinks toward zero.

2 · Set Up

1. Open the hyperopia-corrected preset and press Reset. The corrective converging lens has f = 33 cm.
2. Enable the corrective lens's image-distance readout.
3. Set the true (close) object distance for each trial and record the virtual image distance formed by the corrective lens.

3 · Collect Data

Plot image distance d_i (y-axis) against object distance d_o (x-axis) for your three trials. Does |d_i| grow sharply as d_o approaches 33 cm?

4 · Analyze

1. For one trial, compute d_i from 1/f = 1/d_o + 1/d_i using f = 33 cm. Compare to the table.
2. Explain why, for an object distance well under the focal length (as in all three trials here), the lens forms a distant virtual image — bringing a too-close object 'out' to where the hyperopic eye can actually focus on it.

5 · Extend

1. Compute magnification m = −d_i/d_o for each of your trials. Explain why reading glasses with this kind of setup also enlarge the apparent size of what you're reading, as a side effect of moving its virtual image farther away.
2. This lens's f = 33 cm roughly matches the corrective power needed for a near point around 100 cm (check against the hyperopia experiment's formula: P = 4 − 1 = 3 D, so f = 1/3 m ≈ 33 cm). Confirm these describe the same lens two ways.

The Physics Behind This Experiment

← Back to experiment