The figure shows the image formation of an object in simple microscope. (a) Find out the object distance and image distance from the figure. (b) Derive an equation for magnifying power of the simple microscope. (1 + 2)

![a simple microscope ray diagram forming a virtual magnifie

Question

The figure shows the image formation of an object in simple microscope. (a) Find out the object distance and image distance from the figure. (b) Derive an equation for magnifying power of the simple microscope. (1 + 2)

![a simple microscope ray diagram forming a virtual magnified erect image with angles alpha and beta at the eye — Class 12 Physics question](/figures/ray-optics-and-optical-instruments/simple-microscope-virtual-image-alpha-beta-fig-pyq-ptsk0f.svg)

Accepted Answer

>

> [!TLDR]
> In the figure, $u$ is the object's distance from the lens (just inside the focus) and $v$ is the virtual image's distance from the lens; the magnifying power works out to $m = 1+D/f$ when the image is formed at the near point.
>
> **(a) Object and image distances from the figure:** The object $PQ$ is placed between the lens centre $O$ and its focus $F$, so the object distance is $u = OQ$ (with $u < f$). The refracted rays diverge after the lens and appear to come from the virtual, erect, magnified image $P_1Q_1$ formed on the *same side* as the object; its distance from the lens is the image distance $v = OQ_1$ (with $v > u$, and by lens sign convention both $u$ and $v$ are negative as measured from $O$, but their magnitudes obey $v>u$).
>
> **(b) Deriving the magnifying power:** Angular magnification is defined as the ratio of the angle $\beta$ subtended by the image (through the lens) to the angle $\alpha$ subtended by the object when viewed directly at the near point $D$ (both angles measured at the eye, and for small angles $	an	heta \approx 	heta$):
> $$m = \frac{\beta}{\alpha} = \frac{h/v}{h/D} = \frac{D}{v}\cdot\frac{v}{u}\cdot\frac{u}{1}$$
> More directly, since $\beta \approx h/u$ (angle subtended at the eye close to the lens by the image, essentially at the object's own transverse size $h$ over distance $u$) — using similar triangles at the lens, $m = v/u$ in general.
> …

Q.The figure shows the image formation of an object in simple microscope.

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.The figure shows the image formation of an object in simple microscope.

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