Human stereoscopic acuity — smallest discernible depth from geometry of vision Assuming normal vision with viewing distance 25 cm, smallest resolvable angular disparity of about 20 arcseconds, and interocular distance 6.5 cm, what is the smallest depth difference that can be distinguished?

Introduction / Context:
Stereoscopic vision detects depth from the small angular difference (binocular disparity) of the lines of sight from the two eyes. The fineness of depth perception is important in stereoscopic plotting and 3D visual interpretation.

Given Data / Assumptions:

• Viewing distance s = 25 cm = 0.25 m.
• Interocular distance i = 6.5 cm = 0.065 m.
• Smallest angular disparity α = 20 arcseconds.
• Small-angle approximations apply.

Concept / Approach:

For small disparities, geometric relations give approximately: α ≈ i * Δz / s^2, where Δz is the smallest discernible depth difference at range s. Rearranging yields Δz ≈ α * s^2 / i. Convert α to radians for computation.

Step-by-Step Solution:

Verification / Alternative check:

The order-of-magnitude (tenths of a millimeter at 25 cm) aligns with psychophysical measurements of stereoacuity under good illumination and contrast.

Why Other Options Are Wrong:

• 0.5 to 1.1 mm are larger than the theoretical threshold and would be easily discerned at the given geometry.

Common Pitfalls:

• Using degrees instead of radians in the formula leads to large errors.
• Confusing viewing distance with interocular distance in the relation.

Final Answer:

0.1 mm.