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The image formed by a convex mirror of focal length $30 \mathrm{cm}$ is the quarter of size of the object. Then the distance of the object from the mirror is,(A) $30 \mathrm{cm}$ (B) $90 \mathrm{cm}$ (c) $120 \mathrm{cm}$ (D) $60 \mathrm{cm}$

Last updated date: 17th Jun 2024
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We know that a convex mirror is a spherical reflecting surface or any reflecting surface fashioned into a portion of a sphere in which its bulging side faces the source of light. Automobile enthusiasts often call it a fish eye mirror while other physics texts refer to it as a diverging mirror. Convex mirrors always form images that are upright, virtual, and smaller than the actual object. They are commonly used as rear and side view mirrors in cars and as security mirrors in public buildings because they allow us to see a wider view than flat or concave mirrors. Convex mirrors are used inside the buildings, they are also used in making lenses of sunglasses, they are used in the magnifying glass, they are used in securities and they are used in telescopes.

We know that, The focal length of the convex mirror is $\mathrm{f}=30 \mathrm{cm}$ and the magnification of the image is $\mathrm{m}=1 / 4$
We have to calculate the object distance u. According to sign convention, the measurements along the direction of light are taken as positive and opposite to the light taken as negative. The transverse measurement above the principal axis is taken as positive and below the principal axis is taken as negative. Thus, $f=+30 \mathrm{cm}$ and $\mathrm{m}=+1 / 4=+0.25$
Using formula, $\mathrm{m}=\dfrac{\mathrm{f}}{\mathrm{f}-\mathrm{u}}$
or $\mathrm{mf}-\mathrm{mu}=\mathrm{f}$
or $\mathrm{u}=\dfrac{\mathrm{mf}-\mathrm{f}}{\mathrm{m}}=\dfrac{\mathrm{m}-1}{\mathrm{m}} \mathrm{f}=\dfrac{0.25-1}{0.25}(30)=-90 \mathrm{cm}$