With the help of a ray diagram, describe the construction, working of a compound microscope when the final image is formed at the least distance of distinct vision (D = 25 cm). Derive an expression for the magnifying power. (3+2)

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![Figure — Stem explicitly asks for a ray diagram of a compound microscope with the final image at the least distance of](/figures/ray-optics-and-optical-instruments/ray-formation-image-compound-microscope-fig-9-24.svg) > > [!TLDR] > A compound microscope magnifies in two stages - a real image from the objective, then a magnified virtual image of that from the eyepiece - giving a combined magnifying power m = (L/fo)(1 + D/fe) when the final image is at the near point. > > **Construction:** A compound microscope has two convex lenses of short focal length: the **objective** (very short focal length $f_o$, facing the object) and the **eyepiece** (short focal length $f_e$, close to the eye), mounted at the two ends of a tube, separated by a distance called the tube length L. > > **Working:** The object AB is placed just beyond the focus of the objective ($f_o < u_o < 2f_o$), so the objective forms a **real, inverted, and magnified** image $A'B'$ (this is the first stage of magnification). This intermediate image $A'B'$ then acts as the object for the eyepiece. The eyepiece is positioned so that $A'B'$ falls within its focal length, so the eyepiece acts as a simple magnifying glass, forming a further magnified, **virtual, inverted** (relative to the original object) final image $A''B''$. For the case asked here, the eyepiece is adjusted so this final image forms at the near point (least distance of distinct vision, D = 25 cm), giving maximum magnification for that configuration (called 'normal adjustment when at D'). > > **(Ray diagram, described):** Rays from the object pass through the objective lens converging to form a real inverted image beyond $2f_o$ region within the tube; these diverging rays from that image then strike the eyepiece and, since the image lies inside the eyepiece's focal length, emerge as a divergent bundle that appears to come from a large virtual image at distance D from the eye. > > **Derivation of magnifying power:** > Magnifying power is t

Q.With the help of a ray diagram, describe the construction, working of a compound microscope when the final image is formed at the least distance of distinct vision (D = 25 cm). Derive an expression for the magnifying power. (3+2)

Concept understanding — Microscope Magnification

Microscope Magnification

How the two lenses work together

The objective's magnification

The eyepiece's magnification

Total magnifying power

Worked example

Why this formula?

Microscope Magnification: Why the Formula Holds

1. What Does "Magnification" Mean in a Microscope?

2. The Key Formula

3. Derivation of Objective Magnification $M_o$

Step 1: How the objective works

Step 2: Using the lens formula

Step 3: The tube length approximation

Step 4: Magnification formula

4. Derivation of Eyepiece Magnification $M_e$

Step 1: The eyepiece as a simple magnifier

Step 2: Angular magnification

Q.With the help of a ray diagram, describe the construction, working of a compound microscope when the final image is formed at the least distance of distinct vision (D = 25 cm). Derive an expression for the magnifying power. (3+2)

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