Previously, we reported that the hypomagnetic field obtained by the 100-fold deprivation of the geomagnetic field affected human cognitive processes as estimated in four different cognitive tests. The 40-minute exposure to the hypomagnetic field caused a statistically significant increase both in the task processing time and in the number of errors. The magnetic effect averaged over 40 healthy subjects was about 1.7%. In the present work, the results of a simultaneous study are described, in which the right eye of each subject was video recorded, while the subject performed the tasks. The pupil size increased in the hypomagnetic field. This effect has been calculated by processing the large data set of a few million video frames. The average magnetic effect was about 1.6% (<<0.01, ANOVA, factor of subjects - fixed). Given the heterogeneity, the effect was close to being significant (0.07, ANOVA, factor of subjects - random). The simultaneous recordings of magnetic reactions both for the different cognitive tests and for the eye pupil size were not correlated. These findings provide experimental confirmation of the random nature of the non-specific magnetic biological effects in humans.