B

Step 1: In an astronomical telescope, the total length of the tube is given by the sum of the focal lengths of the objective lens (F_o) and the eyepiece lens (F_e).
Step 2: When an erecting lens with focal length f is introduced, it alters the arrangement of the lenses.
Step 3: The new effective length of the telescope becomes F_o + F_e + f, since we have added the erecting lens in the tube.
Step 4: Typically, F_o (focal length of the objective) is assumed to be equal to the focal length of the eyepiece (F_e) in order to keep the system in balance. Hence, this results in an additional increase of f for the erecting lens.
Step 5: Therefore, if we initially had a telescope of length F_o + F_e, after adding the erecting lens, the change in the length of the telescope tube is equal to f. This actually doubles the effective length (F_o + F_e + f), making it significant relative to the original tube length.
Therefore, the total increase in telescope length is 2f.
Hence, the correct answer is Option B.