To determine the image distance for a convex lens, the lens formula is applied:
\[
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]
Parameters are defined as:
- \( f = 20 \, \text{cm} \) (focal length, positive for a convex lens)
- \( u = -30 \, \text{cm} \) (object distance, negative as the object is on the incident light's side)
- \( v \) represents the image distance to be calculated.
The lens formula is rearranged to solve for \( v \):
\[
\frac{1}{v} = \frac{1}{f} + \frac{1}{u}
\]
Substituting the known values yields:
\[
\frac{1}{v} = \frac{1}{20} + \frac{1}{-30}
\]
This simplifies to:
\[
\frac{1}{v} = \frac{1}{20} - \frac{1}{30}
\]
Using a common denominator (60), the equation becomes:
\[
\frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{3 - 2}{60} = \frac{1}{60}
\]
Therefore, the image distance is:
\[
v = 60 \, \text{cm}
\]
The positive value of \( v \) signifies that the image is formed on the side of the lens opposite to the object, consistent with a real image formed by a convex lens when the object is beyond the focal point.
Consequently, the image distance from the lens is \( 60 \, \text{cm} \).