With a horizontal magnifier before one eye, a frontoparallel surface appears rotated about a vertical axis (geometric effect). With a vertical magnifier, apparent rotation is opposite in direction (induced effect); to restore appearance of frontoparallelism, the surface must be rotated away from the magnified eye. The induced effect is interesting because it was thought until recently that vertical disparities do not play an important role in surface perception. As with the geometric effect, the required rotation for the induced effect increases linearly to ≃ 4% magnification; unlike the geometric effect, it plateaus at ~ 8%. Current theory explains the linear portion: vertical size ratios (VSRs) are used to compensate for changes in horizontal size ratios (HSRs) that accompany eccentric gaze, so changes in VSR cause changes in perceived slant. The theory does not explain the plateau. We demonstrate that it results from differing slant estimates obtained by use of various retinal and extra-retinal signals. When perspective cues to slant are minimized or sensed eye position is consistent with VSR, the induced and geometric effects have similar magnitudes even at large magnifications.
Banks, M. S., & Backus, B. T. (1998). Extra-retinal and perspective cues cause the small range of the induced effect. Vision Research, 38(2), 187–194. https://doi.org/10.1016/S0042-6989(97)00179-X