Question

Deduce the expression m= f/f+u for a spherical lens [where symbols have their usual meaning].​

Answer 1

To derive:

m = f/(f + u) , for a lens .

Derivation:

We know that : for a lens, the magnification is equal to the ratio of the image distance and object distance.

Applying Len's Equation:

$\rm \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

Multiplying numerator on both sides with 'u':

$\rm \implies \dfrac{u}{f} = \dfrac{u}{v} - \dfrac{u}{u}$

$\rm \implies \dfrac{u}{f} = \dfrac{u}{v} - 1$

• u/v can be written as 1/m.

$\rm \implies \dfrac{u}{f} = \dfrac{1}{m} - 1$

$\rm \implies \dfrac{u}{f} + 1 = \dfrac{1}{m}$

$\rm \implies \dfrac{u + f}{f} = \dfrac{1}{m}$

$\rm \implies m = \dfrac{f}{f + u}$

[Hence Derived].