Answer: Light can influence gene expression at caterpillar stage which can further influence butterfly wing development. This hypothesis was proved by Thomas Hunt Morgan in 1917 a biologist who conducted studies on butterflies from two different species : Vanessa urtica and Vanessa io caterpillars under red, green, or blue light whereas other caterpillars were kept in the dark. He found that there were differences in color and size of wings of butterflies exposed to different light conditions. Exposure to red light resulted in bright colored wings while exposure to green light resulted in dusky wings. Blue light and dark light resulted in paler colored wings. Also, V. urtica caterpillars reared under blue light and V.io butterflies reared in dark wings developed were larger in size.
Therefore light which is an external environmental factor can influence gene expression which can further influence phenotype of the organism.
Hence in the given situation butterfly would show differences in their wing color if in the caterpillar stage they were grown in dark or bright white light.