91Ó°ÊÓ

$\frac{1}{S}+\frac{1}{S^{\text{'}}}=\frac{1}{f}$

Where s = object distance from the lens

S' = image distance from the lens

f = focal length of the lens

Sign rules for the variables:

1. Sign rule for the object distance: when the object is on the same side of the refracting surface as the incoming light, object distance s is positive; otherwise, it is negative.
2. Sign rule for the image distance: when the image is on the same side of the refracting surface as the outgoing light, image distance s' is positive; otherwise, it is negative.

$$\begin{gathered} M=\frac{s\text{'}}{f} \\ =\frac{25}{6} \\ =4.1667 \end{gathered}$$

Use the formula,

$$\begin{gathered} \frac{1}{s}+\frac{1}{s\text{'}}=\frac{1}{f} \\ ⇒\frac{1}{s}=\frac{1}{f}-\frac{1}{s^{\text{'}}} \\ ⇒\frac{1}{s}=\frac{1}{6}-\frac{1}{-25} \\ =\frac{31}{150cm} \\ ⇒s=\frac{150}{31} \\ =4.839cm \end{gathered}$$

Thus, the angular magnification obtained is 4.1667 and the object distance from the lens should be 4.839 cm.