Establish the relation 1/f = 1/v - 1/u for a convex lens, where symbols have their usual meanings.

**OR**

Draw a labelled diagram of simple microscope and establish an expression for the magnifying power of simple microscope, when the image formed at (i) Infinity (ii) Least dis

Question

Establish the relation 1/f = 1/v - 1/u for a convex lens, where symbols have their usual meanings.

**OR**

Draw a labelled diagram of simple microscope and establish an expression for the magnifying power of simple microscope, when the image formed at (i) Infinity (ii) Least distance of distinct vision.

Accepted Answer

![Figure — The OR alternative answered says 'Draw a labelled diagram of simple microscope' (hard draw gate); the catalog](/figures/ray-optics-and-optical-instruments/simple-microscope-magnifying-lens-located-image-near-fig-9-23.svg)

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> [!TLDR]
> The thin lens formula follows from applying single-surface refraction twice, once at each face; alternatively, a simple microscope's magnifying power is D/f (image at infinity) or 1+D/f (image at near point).
>
> **Deriving 1/f = 1/v − 1/u for a convex lens**
> Consider a thin convex lens with two spherical refracting surfaces of radii $R_1$ and $R_2$, made of a material of refractive index $n_2$ placed in a medium of refractive index $n_1$. Light from an object at distance $u$ refracts first at surface 1 to form an intermediate (virtual) image at distance $v_1$, given by the single-surface refraction formula:
> $$\frac{n_2}{v_1}-\frac{n_1}{u}=\frac{n_2-n_1}{R_1}$$
> This intermediate image acts as the object for the second surface, refracting back into medium $n_1$ to form the final image at $v$:
> $$\frac{n_1}{v}-\frac{n_2}{v_1}=\frac{n_1-n_2}{R_2}$$
> Adding these two equations (the $n_2/v_1$ terms cancel):
> $$\frac{n_1}{v}-\frac{n_1}{u} = (n_2-n_1)\left(\frac{1}{R_1}-\frac{1}{R_2}ight)$$
> Dividing by $n_1$ and writing $n = n_2/n_1$ (relative refractive index of the lens material):
> $$\frac{1}{v}-\frac{1}{u} = (n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}ight)$$
> When the object is at infinity ($u	o\infty$), $v = f$, the focal length, giving the lensmaker's equation $\frac{1}{f}=(n-1)\left(\frac1{R_1}-\frac1{R_2}ight)$. Substituting the right-hand side by $1/f$ in the general relation above gives the familiar thin lens formula:
> $$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$$
>
> **OR: Magnifying power of a simple microscope** …

Q.Establish the relation 1/f = 1/v - 1/u for a convex lens, where symbols have their usual meanings. OR Draw a labelled diagram of simple microscope and establish an expression for the magnifying power of simple microscope, when the image formed at

Concept understanding — Thin Lens Formula

The Thin Lens Formula: Why a Lens Behaves the Way It Does

The Intuition: Bending Light Systematically

The Precise Statement

What the Formula Tells You

Q.Establish the relation 1/f = 1/v - 1/u for a convex lens, where symbols have their usual meanings. OR Draw a labelled diagram of simple microscope and establish an expression for the magnifying power of simple microscope, when the image formed at

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