Question

What would be the magnification (more than 1 / less than 1 / equal to 1) if the object is placed between F and 2F of the above lens?

Hint:

Memorize the image formation table for a convex lens. Object at 2F \(\rightarrow\) Image at 2F, \(m=1\). Object between F and 2F \(\rightarrow\) Image beyond 2F, \(m>1\). Object beyond 2F \(\rightarrow\) Image between F and 2F, \(m<1\).

Answer 1

Step 1: Recall Image Formation by a Convex Lens:
For a convex lens, when an object is placed between the focal point (F) and twice the focal length (2F), the image is formed beyond 2F. The image is real, inverted, and magnified.
Step 2: Define Magnification:
The linear magnification (\(m\)) produced by a lens is given by the ratio of the image distance (\(v\)) to the object distance (\(u\)).
\[ m = \frac{v}{u} \] The size of the magnification (magnitude) is given by \(|m| = \frac{|v|}{|u|}\).
Step 3: Apply the Condition:
When the object is placed between F and 2F:
- Object distance: \(F<|u|<2F\)
- Image distance: \(|v|>2F\)
Comparing the magnitudes, we clearly see that the image distance is greater than the object distance:
\[ |v|>|u| \] Therefore, the magnitude of the magnification will be:
\[ |m| = \frac{|v|}{|u|}>1 \] Step 4: Final Answer:
Since the image is magnified, the magnification is more than 1.