Find Focal Length of Mirror with 9.5 Magnification, 14mm from Object

AI Thread Summary
To find the focal length of a mirror with a magnification of 9.5 at an object distance of 14mm, the initial calculation using M = v/u yields a virtual image distance (v) of 133mm. Applying the lens formula 1/f = (1/v) + (1/u) results in a focal length (f) of approximately 12.67mm. However, this value is incorrect as it suggests the image is outside of 2f, where no magnification occurs. A revised equation, M = -S2/S1 = f/(f - S1), leads to a focal length of 15.65mm. The calculations indicate that the focal length must be greater than half the virtual image distance to achieve the desired magnification.
Ry122
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A mirror is required with magnification 9.5 when an object is 14mm from the mirror
What is the focal length

My attempt:
M=v/u
9.5=v/14
v=133

1/f = (1/v)+(1/u)
1/f=(1/133)+(1/14)
f=12.67

Since no object is magnified when the created image is outside of 2f
this answer can't be correct.
 
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The answer I get is 15.65.
 
2x15.65 is still less than 133
 
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