How does polarity affect SN1 reactions?

In ##S_N1## reactions, there is a so-called carbocation intermediate. Solvents of higher polarity tend to stabilize these carbocations and therefore, ##S_N1## reactions occur more readily in polar solvents.
For many problems in organic chemistry, it is often a good idea to take a look at the mechanism in question. Here is the mechanism for a general ##S_N1## reaction.
The first step involves bromine as leaving group breaking away to generate the carbocation (positively charged carbon compound). Once the carbocation is formed, the ##CH_3CH_2OH## nucleophile quickly attacks at the positively charged carbon. Notice that since the first step is slow – namely, the formation of carbocation – it will determine the overall rate of the reaction. The more favorable the carbocation formation, the faster the rate of the overall ##S_N1## reaction.
Looking at solvent polarity, as a general rule, a highly polar solvent will stabilize a charged ionic species such as a carbocation much better than a non-polar solvent. This is because the solvent itself has partial positive and partial negative regions (i.e. dipole moments ) which could interact favorably with the charged carbocation.