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[LENS] Given focal length and height, find object distance

1. The problem statement, all variables and given/known data
An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m?

2. Relevant equations
M = Yi/Yo = q/p
1/p+1/q=1/f

Yi= height of the image
Yo = height of the object
q = distance of the image
p= distance of the object
M = magnification
f = focal distance

3. The attempt at a solution

M = Yi/Yo = 0.25 since the image is 25% the height of the object.
Then, since M=q/p, I know the distance from the object to the mirror is 4 times the distance of the image to the mirror.
This is where I'm stuck.
 

ehild

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1. The problem statement, all variables and given/known data
An object is in front of a convex mirror. We then obtain an erect image whose height is equal to 25% of the height of the object. What is the distance between the object and the mirror if we know that the focal distance is equal to 0.2m?

2. Relevant equations
M = Yi/Yo = q/p
1/p+1/q=1/f

Yi= height of the image
Yo = height of the object
q = distance of the image
p= distance of the object
M = magnification
f = focal distance

3. The attempt at a solution

M = Yi/Yo = 0.25 since the image is 25% the height of the object.
Then, since M=q/p, I know the distance from the object to the mirror is 4 times the distance of the image to the mirror.
This is where I'm stuck.
Use the equation you included 1/p+1/q=1/f. Take care of the signs of focal length and image distance.
 

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