Q26. An astronomical telescope has fₒ = 100 cm and fₑ = 5 cm and is initially in normal adjustment. A myopic observer with far point 50 cm views without spectacles. To see sharply with the eye relaxed, the eyepiece must move approximately:
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Question

Q26. An astronomical telescope has fₒ = 100 cm and fₑ = 5 cm and is initially in normal adjustment. A myopic observer with far point 50 cm views without spectacles. To see sharply with the eye relaxed, the eyepiece must move approximately:

Options

G1 Physics · Accepted Answer

GIVEN: Telescope fₒ = 100 cm, fₑ = 5 cm. Myopic observer's relaxed-eye far point = 50 cm. Assume eye close to eyepiece. Step 1: Initially image is at infinity: intermediate-image distance from eyepiece s₁ = fₑ = 5 cm. Step 2: For relaxed myopic vision, eyepiece must create a virtual final image at vₑ = −50 cm. Step 3: With uₑ = −s₂: 1/5 = −1/50 + 1/s₂ ⇒ 1/s₂ = 1/5 + 1/50 = 11/50. Step 4: s₂ = 50/11 = 4.54545 cm. Step 5: Objective and its intermediate image stay fixed. Shift eyepiece towards obj…