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Find the location to the object which when placed in front of a convex mirror produces an image half the access to the object give in the focal length of a convex is half and convex mirror means m is equal to 1/2?
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Solution:


Given:


  • Focal length of convex mirror = f/2

  • Object distance from mirror = x

  • Image distance from mirror = x'

  • Magnification of mirror = m = -1/2



Formula used:


  • Magnification formula: m = - v/u

  • Mirror formula: 1/f = 1/v + 1/u



Calculation:

Given, m = -1/2

Since, m = - v/u

Therefore, -1/2 = -x'/x

Multiplying both sides by x, we get:

x' = x/2

Now, using mirror formula:

1/f = 1/v + 1/u

Since, f = f/2 (given)

Therefore, 1/(f/2) = 1/v + 1/x

Solving for v, we get:

v = 2x/(3/2) = 4x/3

Image distance from mirror = v = 4x/3


Answer:

The location of the object from the convex mirror is x, and the image distance from the mirror is 4x/3.
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