The internal defects in $(CaF_2)$ single crystal were characterized by the observation of optical microscopy, the element analysis and the transmittance analysis. In bubble and negative crystal which are composed to crystal plane of (100) and (111), the spread negative crystal in $(CaF_2)$ crystal gave an effect of low transmittance. The precipitates formed in bubble as internal cavities were analyzed by using WDX. Violet colored-crystal had higher a dislocation density than non-colored crystal, and the atomic ratio between Ca and F changed by poor F ion. In this result, we could determine indirectly that violet color was occurred by poor F ion.