A camera lens has a focal length of 200mm . How far from the lens should the subject for the photo be if the lens is 20.4cm from the sensor?

An optical lens is a transparent transmissive optical component that is used to either converge or diverge the light emitting from a object. These transmitted light forms an image of that object.

Thin Lens formula:

$\frac{\mathbf{1}}{\mathbf{u}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{v}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{f}}$

Here,

u = Object distance from lens

v = Image distance from lens

f = Focal length of the lens

Sign Convention:

1. Object Distance (u): (+) in front of lens; (-) in the back of lens
2. Image Distance (v): (-) in front of lens; (+) in the back of lens
3. Focal Length (f): (+) for convergent (convex) lens; (-) for divergent (concave) lens

Focal length of 1^st lens$f_1=+20cm$

Image distance, $v=+20.4cm$

By using lens formula

$$\begin{gathered} \Rightarrow \frac{1}{u}+\frac{1}{v_1}=\frac{1}{f_1} \\ \Rightarrow \frac{1}{v_1}+\frac{1}{+20.4}=\frac{1}{+20} \\ \Rightarrow \frac{1}{v_1}=\frac{1}{+20}-\frac{1}{+20.4} \\ \Rightarrow \frac{1}{v_1}=\frac{0.4}{20*}20.4 \\ \Rightarrow v_1=+1020cmor10.2m \end{gathered}$$

Therefore, the lens should be 10.2m from the object.