A person is standing x cm away from concave security mirror in a store, if the person's image appears to be three times taller than the actual person which is virtual and if the radius of curvature of the mirror is 48 cm, then find x?-12 cm-16 cm-13.33 cm-26.66 cm
Question
A person is standing x cm away from concave security mirror in a store, if the person's image appears to be three times taller than the actual person which is virtual and if the radius of curvature of the mirror is 48 cm, then find x?-12 cm-16 cm-13.33 cm-26.66 cm
Solution
To solve this problem, we need to use the mirror formula and magnification formula for concave mirrors.
The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.
Given that the image is three times the size of the object, we know that m = -3.
We also know that the radius of curvature is 48 cm. The focal length of a mirror is half its radius of curvature, so f = 48/2 = 24 cm.
We can substitute these values into the mirror formula:
1/24 = 1/v + 1/u
We can also substitute the values into the magnification formula:
-3 = -v/u
From the magnification formula, we can express v in terms of u:
v = 3u
Substitute v = 3u into the mirror formula:
1/24 = 1/(3u) + 1/u 1/24 = 4/(3u) 3u = 96 u = 96/3 = 32 cm
So, the person is standing 32 cm away from the mirror. This is not one of the options given, so there may be a mistake in the problem or the answer choices.
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