Given a convex lens with focal length \( f = 20 \, \text{cm} \) and an object at \( u = -30 \, \text{cm} \). Determine the image position.
Step 1: Apply the lens formula
The lens formula is:
\[\
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\
\]\
Solving for \( v \):
\[\
\frac{1}{v} = \frac{1}{f} + \frac{1}{u}\
\]\
Step 2: Substitute known values
Plugging in the given values:
\[\
\frac{1}{v} = \frac{1}{20} + \frac{1}{-30}\
\]\
\[\
\frac{1}{v} = \frac{1}{20} - \frac{1}{30}\
\]\
Using the LCD of 60:
\[\
\frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60}\
\]\
Step 3: Calculate \( v \)
\[\
v = 60 \, \text{cm}\
\]\
Step 4: Conclusion
The image is located \( 60 \, \text{cm} \) from the lens, on the side opposite the object, forming a real, inverted image.
Answer: The image position is \( 60 \, \text{cm} \).