Q42. An astronomical telescope with fₒ = 80 cm and fₑ = 5 cm observes an object 64.8 m from the objective. The final image is at infinity. Required tube length is:
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Q42. An astronomical telescope with fₒ = 80 cm and fₑ = 5 cm observes an object 64.8 m from the objective. The final image is at infinity. Required tube length is:

G1 Physics · Accepted Answer

GIVEN: Telescope fₒ = 80 cm, fₑ = 5 cm; finite object distance from objective = 64.8 m = 6480 cm; final image at ∞. Step 1: For the objective, uₒ = −6480 cm and fₒ = +80 cm. Step 2: Lens formula: 1/80 = 1/vₒ − (−1/6480) = 1/vₒ + 1/6480. Step 3: 1/vₒ = 1/80 − 1/6480 = (6480 − 80)/(80 × 6480) = 6400/(80 × 6480). Step 4: vₒ = (80 × 6480)/6400 = 81 cm (slightly beyond the 80 cm focal plane). Step 5: Final image at infinity requires intermediate image 5 cm in front of eyepiece: L = vₒ + fₑ = 81 + 5…