Q31. A compound microscope has objective focal length 1 cm, eyepiece focal length 5 cm and total angular magnification magnitude 100 in normal adjustment (D = 25 cm). The distance between the lenses is:
Options

Question

Q31. A compound microscope has objective focal length 1 cm, eyepiece focal length 5 cm and total angular magnification magnitude 100 in normal adjustment (D = 25 cm). The distance between the lenses is:

Options

G1 Physics · Accepted Answer

GIVEN: Compound microscope fₒ = 1 cm; fₑ = 5 cm; total angular magnification magnitude 100; D = 25 cm; final image at ∞. Step 1: Eyepiece magnification mₑ = D/fₑ = 25/5 = 5. Step 2: Required objective magnification magnitude |mₒ| = |M|/mₑ = 100/5 = 20. Step 3: For a real objective image, |mₒ| = vₒ/fₒ − 1 ⇒ 20 = vₒ/1 − 1. Step 4: vₒ = (20 + 1) × 1 = 21 cm. Step 5: For final image at ∞, lens separation L = vₒ + fₑ = 21 + 5 = 26 cm. FINAL ANSWER: Tube length = 26 cm. Option C.