Answer
3.0 m.
Work Step by Step
The star is essentially at infinity. The image of the star created by the objective mirror will be located at the focal length of the objective, or one-half the radius of curvature (equation 23–1).
$$d_{i1}=f_o=\frac{R_o}{2}=\frac{3.00m}{2}=1.50m$$
Subtract this distance from the distance between the mirrors, and we’re left with the object distance for the second mirror.
$$d_{o2}=\ell-d_{i1}=0.90m-1.50m=-0.60m$$
Use the mirror equation to calculate the final image distance. This is which is where the sensor should be located.
$$\frac{1}{d_{o2}}+\frac{1}{d_{i2}}=\frac{1}{f_e}=\frac{2}{R_e}$$
$$\frac{1}{-0.60m }+\frac{1}{d_{i2}}=\frac{2}{-1.50m}$$
$$d_{i2}=3.0m$$
