A student is calibrating an eyepiece graticule on a light microscope using a stage micrometer. The stage micrometer has a total length of 1.00 mm divided into 100 equal divisions.
Using a ×10 \times 10\,×10 objective lens and a ×10 \times 10\,×10 eyepiece lens (total magnification ×100\times 100×100), the student finds that 50 eyepiece graticule divisions align with exactly 40 divisions on the stage micrometer.
The student then changes the objective lens to ×40\times 40×40 (total magnification ×400\times 400×400).
Which option correctly shows the value of one eyepiece graticule division at ×100 \times 100\,×100 magnification, and the value of one eyepiece graticule division at ×400 \times 400\,×400 magnification?
Value at ×100\times 100×100: 8.0 μm8.0\ \mu\text{m}8.0 μm; Value at ×400\times 400×400: 2.0 μm2.0\ \mu\text{m}2.0 μm
Value at ×100\times 100×100: 8.0 μm8.0\ \mu\text{m}8.0 μm; Value at ×400\times 400×400: 32.0 μm32.0\ \mu\text{m}32.0 μm
Value at ×100\times 100×100: 12.5 μm12.5\ \mu\text{m}12.5 μm; Value at ×400\times 400×400: 3.1 μm3.1\ \mu\text{m}3.1 μm
Value at ×100\times 100×100: 12.5 μm12.5\ \mu\text{m}12.5 μm; Value at ×400\times 400×400: 50.0 μm50.0\ \mu\text{m}50.0 μm
