Find the power of a convex lens if the image formed is at a distance of 25 cm from the lens when the object is placed on the other side of the lens at 12 cm from the optical centre?

According to the sign convention for lenses, let the direction of incident light be positive.
Given:

Object distance, u=−12cm=−0.12m (placed on the opposite side of the incoming light relative to the standard image side).

Image distance, v=+25cm=+0.25m (real image on the other side).

Using the lens formula:

f
1
​
=
v
1
​
−
u
1
​

Substituting the values:

f
1
​
=
25
1
​
−(
−12
1
​
)
f
1
​
=
25
1
​
+
12
1
​

f
1
​
=
300
12+25
​
=
300
37
​
cm
−1

Since power P in diopters (D) is given by
f(in cm)
100
​
:

P=
300
37
​
×100=
3
37
​
≈12.33D
As it is a convex lens producing a real image, the power is positive: +12.33diopters.