# Gravitational time dilation using accelerating light-clock

I've been trying to understand gravitational time dilation by considering a light-clock of length $$l$$ undergoing an equivalent acceleration $$a$$ from rest along the direction of the bouncing light pulse.

I find that the time $$t$$ that the light pulse takes to travel to the forward receding mirror and then back to the approaching back mirror is given by

$$t \approx \frac{2l}{c}-\frac{al^2}{c^3}$$

Is this result obviously wrong as it implies that the light clock is taking less time to tick in a gravitational field than the time $$2l/c$$ that it takes without any gravitational field?