Calculations are presented of the lifetime of OH against photodissociation by the interstellar radiation field as a function of depth into interstellar clouds containing grains of various scattering properties. The effectiveness of the different photodissociation channels changes with depth into a cloud. Absorption into the repulsive - state is usually the main dissociation channel, but with forward-scattering grains in clouds of small optical depths, absorption into the 3 2H state is more effective. Subject headings: interstellar: molecules molecular processes