Answer :
Answer:
To find the position of the image formed by a convex lens, we can use the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) = focal length of the lens
- \( v \) = distance of the image from the lens (image distance)
- \( u \) = distance of the object from the lens (object distance)
Given:
- \( f = 24 \) cm
- \( magnification = 6 \)
First, let's find the object distance using the magnification formula:
\[ \text{Magnification} = \frac{-v}{u} \]
Given that the magnification is \( 6 \), we have:
\[ 6 = \frac{-v}{u} \]
\[ u = \frac{-v}{6} \]
Since the magnification is positive, it implies that the image is real and inverted. Now, let's substitute the value of magnification into the lens formula:
\[ \frac{1}{24} = \frac{1}{v} - \frac{1}{\frac{-v}{6}} \]
\[ \frac{1}{24} = \frac{1}{v} + \frac{6}{v} \]
\[ \frac{1}{24} = \frac{7}{v} \]
\[ v = \frac{24}{7} \]
So, the position of the image is \( \frac{24}{7} \) cm from the lens.