Compound MicroscopeJEE Main

Two-stage magnification — objective × eyepiece — interactive Physics simulation for IIT-JEE.

Concept

A compound microscope magnifies twice. The short-focus objective forms a real, enlarged, inverted image of a very close object; the eyepiece then acts as a magnifier on that image. Total magnification is the product — hundreds of × from two modest lenses.

Key formula

M = m_o \times m_e = \frac{v_o}{u_o}\left(1 + \frac{D}{f_e}\right), \qquad M_{relaxed} \approx \frac{L}{f_o}\cdot\frac{D}{f_e}

Derivation

Object just outside $f_o$ → real image near the eyepiece's focal plane, linear magnification $m_o = v_o/u_o$ .

Eyepiece as simple magnifier: angular magnification $1 + D/f_e$ (image at near point D = 25 cm) or $D/f_e$ (relaxed, image at ∞). The approximation $m_o \approx L/f_o$ holds because $v_o \approx L$ and $u_o \approx f_o$ .

Scenarios to explore

Compound Microscope — Objective × eyepiece — two-stage magnification.

Real-world applications

Biology lab microscopes (40×–1000×).
Metallurgical inspection microscopes.
The design template for all two-stage optical instruments.

JEE exam tips

Higher M ⇒ both f₀ and f_e small — inverse dependence on both.
Final image inverted relative to the object (objective inverts, eyepiece doesn't re-invert).
'Image at D' gives the (1 + D/f_e); 'relaxed/normal adjustment' gives D/f_e.

Common mistakes

Adding magnifications instead of multiplying.
Using long-focus objective — microscopes need SHORT f₀ (contrast with telescopes).
Placing the object inside f₀ (virtual image — instrument fails).

Exam traps to avoid

L in M ≈ (L/f₀)(D/f_e) is tube length, not object distance.
Objective magnification is LINEAR; eyepiece contributes ANGULAR magnification.