# How do I derive this physical equation

## Optical lenses

To convert the equation \ [\ frac {\ color {Red} {{B}}} {{{G}}} = \ frac {{{b}}} {{{g}}} \] to \ (\ color {Red} {{B}} \) you have to dissolve **two transformations** carry out:

**Multiply** both sides of the equation with \ ({{G}} \). Write the \ ({{G}} \) on both sides of the equation directly as a numerator in the fractions. \ [\ Frac {\ color {Red} {{B}} \ cdot {{G}}} {{{G }}} = \ frac {{{b}} \ cdot {{G}}} {{{g}}} \]

**Brevity** the fraction on the left side of the equation by \ ({{G}} \). \ [\ color {Red} {{B}} = \ frac {{{b}} \ cdot {{G}}} {{ {g}}} \] The equation is solved for \ (\ color {Red} {{B}} \).

To convert the equation \ [\ frac {{{B}}} {\ color {Red} {{G}}} = \ frac {{{b}}} {{{g}}} \] to \ (\ color {Red} {{G}} \) you have to dissolve **three transformations** carry out:

**Picture** on either side of the equation **the reciprocal** the fractions. \ [\ frac {\ color {Red} {{G}}} {{{B}}} = \ frac {{{g}}} {{{b}}} \]

**Multiply** both sides of the equation with \ ({{B}} \). Write the \ ({{B}} \) on both sides of the equation directly as a numerator in the fractions. \ [\ Frac {\ color {Red} {{G}} \ cdot {{B}}} {{{B }}} = \ frac {{{g}} \ cdot {{B}}} {{{b}}} \]

**Brevity** the fraction on the left side of the equation by \ ({{B}} \). \ [\ color {Red} {{G}} = \ frac {{{g}} \ cdot {{B}}} {{ {b}}} \] The equation is solved for \ (\ color {Red} {{G}} \).

To convert the equation \ [\ frac {{{B}}} {{{G}}} = \ frac {\ color {Red} {{b}}} {{{g}}} \] to \ (\ color {Red} {{b}} \) you have to dissolve **three transformations** carry out:

**Swap** the two sides of the equation. \ [\ frac {\ color {Red} {{b}}} {{{g}}} = \ frac {{{B}}} {{{G}}} \]

**Multiply** both sides of the equation with \ ({{g}} \). Write the \ ({{g}} \) on both sides of the equation directly as a numerator in the fractions. \ [\ Frac {\ color {Red} {{b}} \ cdot {{g}}} {{{g }}} = \ frac {{{B}} \ cdot {{g}}} {{{G}}} \]

**Brevity** the fraction on the left side of the equation by \ ({{g}} \). \ [\ color {Red} {{b}} = \ frac {{{B}} \ cdot {{g}}} {{ {G}}} \] The equation is solved for \ (\ color {Red} {{b}} \).

To convert the equation \ [\ frac {{{B}}} {{{G}}} = \ frac {{{b}}} {\ color {Red} {{g}}} \] to \ (\ color {Red} {{g}} \) you have to dissolve **four transformations** carry out:

**Swap** the two sides of the equation. \ [\ frac {{{b}}} {\ color {Red} {{g}}} = \ frac {{{B}}} {{{G}}} \]

**Picture** on either side of the equation **the reciprocal** the fractions. \ [\ frac {\ color {Red} {{g}}} {{{b}}} = \ frac {{{G}}} {{{B}}} \]

**Multiply** both sides of the equation with \ ({{b}} \). Write the \ ({{b}} \) on both sides of the equation directly as a numerator in the fractions. \ [\ Frac {\ color {Red} {{g}} \ cdot {{b}}} {{{b }}} = \ frac {{{G}} \ cdot {{b}}} {{{B}}} \]

**Brevity** the fraction on the left side of the equation by \ ({{b}} \). \ [\ color {Red} {{g}} = \ frac {{{G}} \ cdot {{b}}} {{ {B}}} \] The equation is solved for \ (\ color {Red} {{g}} \).

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