Question:medium

An object placed at a distance of +15 cm is slowly moved towards the pole of a convex mirror. The image will get

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While a convex mirror always produces a diminished image compared to the actual object size, moving the object closer to the mirror increases the image size relative to its previous state.
At the pole, the image size equals the object size (\(m = 1\)).
  • shortened and real.
  • enlarged and real.
  • enlarged and virtual.
  • diminished and virtual.
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Recall what a convex mirror always does.
A convex mirror always forms a virtual, erect image no matter where the object is kept, because it is a diverging mirror, so the image type will not flip to real at any stage.
Step 2: Test the trend with real numbers.
Take a convex mirror of focal length $f = 15\text{ cm}$, so $f = +15\text{ cm}$. First place the object at $u = -15\text{ cm}$: \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15} + \frac{1}{15} = \frac{2}{15} \implies v = 7.5\text{ cm}, \quad m = -\frac{v}{u} = 0.5 \]
Step 3: Move the object closer and compare.
Now bring the object to $u = -5\text{ cm}$: \[ \frac{1}{v} = \frac{1}{15} + \frac{1}{5} = \frac{4}{15} \implies v = 3.75\text{ cm}, \quad m = -\frac{v}{u} = 0.75 \] Both values of $v$ are positive, meaning the image stays behind the mirror, that is virtual, and the magnification has grown from $0.5$ to $0.75$ as the object came closer.
Step 4: State the trend.
As the object keeps moving towards the pole, the image keeps growing in size while remaining virtual and erect throughout.
\[ \boxed{\text{enlarged and virtual}} \]
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