91Ó°ÊÓ

Thin Lens formula:

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

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

Power of a lens is defined as the reciprocal of its focal length. Thus, converging or convex lens have positive powers and diverging or concave lens have negative powers.

Object distance, u = (+25.0-2)cm

=+23cm

Image distance, v = (+45.0+2)cm

= - 43 cm

By using lens formula,

$$\begin{gathered} ⇒\frac{1}{+23}+\frac{1}{-43}=\frac{1}{f} \\ ⇒\frac{43-23}{43*23}=\frac{1}{f} \\ ⇒f=+45.49cm \end{gathered}$$

Power of the lens is given by

$$\begin{gathered} ⇒Power,P=\frac{1}{Focallength,f} \\ ⇒P=\frac{1}{f}=\frac{100}{49.45}cm \\ =2.022diopters \end{gathered}$$

Therefore, the farsightedness can be corrected by using a converging glasses of focal length +49.45 cm and power +2.022 diopters.