23. A microorganism when viewed under a compound microscope with objective of 10× magnification measured 400 nm in length.
The same microorganism when viewed under a dissecting microscope with 10× lens would measure:
A. 100 m
B. 10 m
C. 40 m
D. 400 nm
Correct Answer: C. 40 μm
A compound microscope with 10× objective typically delivers total magnification of ~100× (10× objective × 10× eyepiece), so the true size of the 400 nm microorganism is 400 nm / 100× = 4 nm actual length. Under a dissecting microscope’s 10× magnification, the image appears 10× larger than actual, measuring 4 nm × 10 = 40 μm.
Detailed Calculation
Step 1: True size from compound microscope
Image size = 400 nm at 10× objective. Standard compound scopes use 10× eyepiece, giving total M = 10× × 10× = 100×.
True length = Image size / Total magnification = 400 nm / 100 = 4 nm.
Step 2: Dissecting microscope measurement
Dissecting (stereo) microscopes provide lower magnification (typically 10×–40× total from 10× objective + eyepiece). At stated “10× lens,” image size = True size × 10 = 4 nm × 10 = 40 × 10⁻⁹ m = 40 μm.
Option Explanations
A. 100 μm: Wrong—assumes ~40× dissecting magnification (4 nm × 25?), overestimating stereo scope power.
B. 10 μm: Wrong—assumes 2.5× magnification, below typical dissecting minimums.
C. 40 μm: Correct—as calculated above for standard 10× stereo optics.
D. 400 nm: Wrong—ignores magnification difference; same image size violates scope comparison.
Microscope Magnification Basics
Microorganism size calculation between compound microscope 10× objective (400 nm image) and dissecting microscope 10× requires understanding total magnification differences—compound ~100× vs stereo ~10×—yielding true size 4 nm and 40 μm image. Essential for GATE Life Sciences optics MCQs.
Magnification Comparison Table
| Microscope Type | Typical Total Mag. | 400 nm Image → True Size | 10× Lens Image Size |
|---|---|---|---|
| Compound (10× obj.) | 100× (10× eyepiece) | 4 nm | N/A |
| Dissecting (Stereo) | 10× | 4 nm | 40 μm |
Exam Formula Application
True size = Measured image / Total M. Dissecting scopes view larger fields at lower power for 3D stereo, unlike compound’s high-res internal focus. Master for microbiology measurement questions.
