The size of the image formed by a convex mirror is half the size of the object, when the latter is held at a distance of from the mirror. ____cm is the radius of curvature of the mirror.

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Detailed Solution

Concept- The radius of curvature of the mirror is 60cm. Using the lens's magnification formula, calculate the picture distance. Find the convex lens's focal length using the lens formula. It ought to be advantageous. The radius of curvature is equal to the lens's focal length times two.
Magnification,

Here,

is the height of the image and

is the height of the object.
Lens formula,

Here,

is the focal length,

is the object distance and

is the image distance.
We have stipulated that the image's size is equal to half the object's size. We have a phrase for the lens's magnification:

Here,

is the height of the image and

is the height of the object.
According to the question,

_______(1)
Additionally, there is an equation for magnification that takes into account object and picture distance.

The image distance in this case is v, while the object distance is u.
Equation (1) in the previous equation yields,