Dear student,
Auxins are not photophilic but shows phototropism. Auxin moves away from light in shoot and root both therefore it is not photophilic rather it shows response to light (phototropism). When sunlight falls on shoot, auxin redistribute itself to the side where sunlight is in less amount and therefore it causes growth and bends the shoot towards sunlight to collect more amount of sunlight. But in root opposite phenomena occurs because auxin redistribute itself towards shaded portion of root which grows less than the portion of root exposed to sunlight and thus causes bending of root towards the ground i.e root shows positive geotropic movement.
Regards