In a reflecting telescope, the focal length of the eyepiece is 5 cm. What should be the radius of curvature of the objective mirror to have a magnifying power of 40?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 m
In a reflecting telescope the objective is a concave mirror, whose focal length is half its radius of curvature, \( f_o=R/2 \). With the final image at infinity, the magnifying power is \( m=f_o/f_e \).
The focal length of the objective mirror is:
\( \begin{aligned} f_o &= m\,f_e \\ &= 40\times5\,\mathrm{cm} \\ &= 200\,\mathrm{cm} \end{aligned} \)
The radius of curvature of the mirror is:
\( \begin{aligned} R &= 2f_o \\ &= 2\times200\,\mathrm{cm} \\ &= 400\,\mathrm{cm} \\ &= 4\,\mathrm{m} \end{aligned} \)