A mirror is used to produce an image with magnification of 
. If the distance between object and its image is 40 cm, then the focal length of the mirror is ______
Text Solution
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Magnification (m):
The magnification is given by the relationship:
Rearrange to find the object distance 
in terms of the image distance (v):
Distance between object and image:
It is given that the sum of the object distance and the image distance is 40 cm :
Substituting 
into the equation gives:
Solving for 
gives:
Find the object distance (u):
Substitute 
back into 
:
Calculate the focal length (f):
Use the mirror formula:
Substituting the values of 
and 
:
Simplify and solve for 
:
Therefore, the focal length is:
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