Q30. The naked human eye resolves a minimum angular separation of 1 arcminute. Through a telescope of angular magnification 30, and assuming its own diffraction limit is negligible, the smallest object angular separation the eye can resolve is:
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Question

Q30. The naked human eye resolves a minimum angular separation of 1 arcminute. Through a telescope of angular magnification 30, and assuming its own diffraction limit is negligible, the smallest object angular separation the eye can resolve is:

Options

G1 Physics · Accepted Answer

GIVEN: Naked eye resolves 1 arcminute; telescope angular magnification |M| = 30. Telescope diffraction is assumed negligible. Step 1: Convert the unaided resolution threshold: 1 arcminute = 60 arcseconds. Step 2: Telescope magnifies apparent angular separation: θₐₚₚ = |M| × θₐ꜀ₜᵤₐₗ. Step 3: At the visibility threshold: 60 arcseconds = 30 × θₐ꜀ₜᵤₐₗ. Step 4: θₐ꜀ₜᵤₐₗ = 60/30 = 2 arcseconds. FINAL ANSWER: 2 arcseconds. Option B.