The board may authorize a variance from the terms of this article when, in its opinion, undue hardship will result from requiring strict compliance. In granting a variance, the board shall prescribe only conditions that it deems necessary for, or desirable to, the public interest. In making the findings hereinbelow required, the board shall take into account the nature of the proposed use of the land involved, existing uses of land in the vicinity, the number of persons who will reside or work within the proposed use, and the probable effect such variance will have upon traffic conditions and upon the public health, safety, convenience and welfare of the village.