C

To find the effective focal length \( f \) of two thin lenses in contact, we use the formula:
Effective focal length:
\[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \]
where \( f_1 \) and \( f_2 \) are the focal lengths of the individual lenses.
Step 1: Remember that for two thin lenses, the effective focal length is calculated by taking the sum of the reciprocals of their individual focal lengths.
Step 2: Rearranging gives us:
\[ f = \frac{f_1 f_2}{f_1 + f_2} \]
Therefore, the correct option representing this relationship is (C), which matches our derived formula.