What is meant by compound microscope? Draw a ray diagram of the formation of an image by a compound microscope. Briefly describe its working and derive the formula for its total magnification. (1+1+1+1=4)

**OR**

What is meant by Telescope? Draw a ray diagram of image formation

Question

What is meant by compound microscope? Draw a ray diagram of the formation of an image by a compound microscope. Briefly describe its working and derive the formula for its total magnification. (1+1+1+1=4)

**OR**

What is meant by Telescope? Draw a ray diagram of image formation by a refracting telescope. Briefly describe its working and derive the formula for its magnifying power.

Accepted Answer

![Figure — The answered alternative (compound microscope) explicitly asks for its image-formation ray diagram; the catalo](/figures/ray-optics-and-optical-instruments/ray-formation-image-compound-microscope-fig-9-24.svg)

>

> [!TLDR]
> A compound microscope magnifies in two stages — the objective forms a real, magnified image close to the eyepiece's focal point, and the eyepiece then acts as a simple magnifier on that intermediate image — multiplying the two individual magnifications together.
>
> **Setup:** A compound microscope has two converging lenses: the **objective**, of short focal length $f_o$, placed close to the (tiny) object; and the **eyepiece**, of somewhat larger focal length $f_e$, through which the observer looks.
>
> *(Ray diagram description: the object O is placed just beyond the objective's focal point F₀, so the objective forms a real, inverted, magnified image I₁ inside the eyepiece's focal length. This image I₁ acts as the object for the eyepiece, which — since I₁ lies within its focal length — forms a large, virtual, further-magnified final image I₂. For normal (relaxed-eye) adjustment, I₁ is placed exactly at the eyepiece's focal point so I₂ forms at infinity; alternatively the eyepiece can form I₂ at the near point D.)*
>
> **Working:** The objective, being of very short focal length and placed just outside its focal length from the object, produces a real, inverted, highly magnified intermediate image $I_1$. This image then serves as the "object" for the eyepiece, which is used essentially as a simple magnifying glass to give a further magnified, virtual final image $I_2$.
>
> **Magnification (final image at the near point D, common derivation):**
>
> Magnification by the objective:
> $$m_o = \frac{v_o}{u_o} \approx \frac{L}{f_o}$$ …

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

🎓Unlock everything free for 14 days

Unlock everything free for 14 days