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An object is placed at a long distance in front of a convex mirror of radius of curvature 30 cm. State the position of its image.
When an object is placed at a long distance in front of a convex mirror of radius of curvature 30 cm, then the position of its image will be 15cm behind the mirror at focus $(F)$.
This is because, in a convex mirror when an object is placed at a long distance or infinity, it forms the image at focus $(F)$.
Explanation
A convex mirror always forms virtual, erect, and diminished images irrespective of the distance between the object and the mirror.
Here, the radius of curvature, $R$ is given 30 cm.
We know that focal length, $f$ is equal to half of the radius of curvature, $R$, which is given as-
$f=\frac {1}{2}\times {R}$
Putting the value of $R$ we get-
$f=\frac {1}{2}\times {30}$
$f=15cm$
Thus, the focal length of the convex mirror is 15 cm.
Hence, the image will form 15 cm behind the mirror at focus, $(F)$.
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