This paper presents an analytical description for the growth of the projected emittance (here just referred to the transverse emittance) based on the concept of the slice emittance in an RF photoinjector. In the RF photoinjector, the slice emittance undergoes small changes, but the projected emittance changes significantly even in the drift space after the injector. Carefully adjusting the parameters of the RF photoinjector, which usually means emittance compensation,the projected emittance can be minimized to the value of the shce emittance. The relation between slice emittance and projected emittance is explained in this paper. An emittance function, which shows such a relation, is also introduced.A model about the emittance growth in the RF photoinjector is established, which accords with the particle simulation results by using the code ASTRA. The condition to minimize the emittance is also given by using the emittance function,which means the emittance compensation in the RF photoinjector.