A

To understand the effect of changing the diameter of a telescope's objective on its resolving power, we start with the formula for resolving power (R) of a telescope, which is given by:
R = \frac{1.22 \lambda}{D}
where:

• \lambda is the wavelength of light.
• D is the diameter of the telescope's objective.

When the diameter of the telescope is increased from 1 meter to 2.54 meters, we can calculate the new resolving power:
R_{new} = \frac{1.22 \lambda}{2.54}
The ratio of the new resolving power to the original resolving power is:
\frac{R_{new}}{R_{old}} = \frac{\frac{1.22 \lambda}{2.54}}{\frac{1.22 \lambda}{1}} = \frac{1}{2.54}
Thus, the resolving power increases by 2.54 times. Therefore, Option A is correct.