75. A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance :

75. A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance :

(a) 37.3 cm

(b) 46.0 cm

(c) 50.0 cm

(d) 54.0 cm

Answer :  (d) 54.0 cm

\(\frac{1}{F_o} = \frac{1}{V_o} - \frac{1}{U_o}\)

\(\frac{1}{+40} = \frac{1}{V_o} - \frac{1}{-200}\)

\(\frac{1}{V_o} = \frac{1}{40} - \frac{1}{200}\)

\(V_o = 50 \, \text{cm}\)

\(50 \, \text{cm} + 4 \, \text{cm} = 54 \, \text{cm}\)