Question

When the object is placed very close to the lens, the image formed is virtual, erect and

• A. diminished
• B. smaller in size
• C. magnified
• D. bigger in size

Hint:

A convex lens acts as a magnifying glass only when the object is placed within its focal length (\(|u| \lt f\)).
The resulting image is virtual, erect, and magnified.

Answer 1

The Correct Option is C

Step 1: Set up a concrete example.
Take a convex lens of focal length $f = 10\text{ cm}$ and place the object well inside the focus, say at $u = -5\text{ cm}$.
Step 2: Apply the lens formula. \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{10} - \frac{1}{5} = -\frac{1}{10} \implies v = -10\text{ cm} \]
Step 3: Read off the nature and size of the image.
Since $v$ is negative, the image forms on the same side as the object, which means it is virtual. Using $m = \dfrac{v}{u} = \dfrac{-10}{-5} = 2$, the image is twice the size of the object and the positive sign tells us it is erect.
Step 4: Generalise this result.
Any time the object is placed well within the focal length of a convex lens, the same pattern repeats, a virtual, erect image that is bigger than the object, which is exactly how a magnifying glass works.
\[ \boxed{\text{magnified}} \]