A student examines a beetle mm tall with a hand lens (a simple magnifier) of focal…
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging
Optics and Photonics, Ch Stops, pupils and optical instruments
Problem
A student examines a beetle 2.00 mm tall with a hand lens (a simple magnifier) of focal length f=40.0 mm. The beetle is held at the focal point of the lens, so the eye viewing through the lens is relaxed and the image is at infinity. The lens is 30 mm across and is held close to the eye, whose pupil is 5 mm wide. The student's laboratory report reads: "Because the virtual image is at infinity, the object and the image both appear the same size, so the angular magnification is MA=1. Furthermore, since MA is small, the lens does not gather any extra light, so the magnifier makes no difference to how bright the beetle looks."
((a)) Explain what is wrong with the student's calculation of MA, and calculate the correct value, using the standard near point d0=250 mm.
((b)) Explain what is wrong with the student's reasoning about brightness, referring to what actually controls how much light reaches the eye, and say whether the conclusion that the beetle looks no brighter survives.