Q40. An astronomical telescope has fₒ = 120 cm and fₑ = 6 cm. The final image must be 30 cm in front of the eyepiece. The required tube length is:
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Question

Q40. An astronomical telescope has fₒ = 120 cm and fₑ = 6 cm. The final image must be 30 cm in front of the eyepiece. The required tube length is:

G1 Physics · Accepted Answer

GIVEN: Astronomical telescope fₒ = 120 cm, fₑ = 6 cm; final image lies 30 cm in front of eyepiece (virtual). Step 1: Eyepiece final-image distance vₑ = −30 cm; intermediate-image distance uₑ = −s. Step 2: Lens formula: 1/6 = −1/30 + 1/s ⇒ 1/s = 1/6 + 1/30. Step 3: 1/s = (5 + 1)/30 = 6/30 = 1/5 ⇒ s = 5 cm. Step 4: Distant object gives objective intermediate image at fₒ = 120 cm. Step 5: Required tube length L = fₒ + s = 120 + 5 = 125 cm. FINAL ANSWER: 125 cm. Option B.