# The distance between an object and its upright image is d. If the magnification is M, what is the focal length of the lens being used to form the image?

+7 votes

The distance between an object and its upright image is d. If the magnification is M, what is the focal length of the lens being used to form the image? (Use any variable or symbol stated above as necessary.)

If M < 1
f =

If M > 1
f =

asked Apr 9, 2012 in Physics

## 1 Answer

+5 votes

Best answer

Magnification M is defined as :

M = - q / p

(*where q=image distance, p=object distance)

we can further solve this equation for q, (which is needed later on).

q = - M*p

Based on the properties on lens, we can conclude that for M<1 it is a diverging lens, and the image is virtual.

Here are some basic sign conventions for reference:

the distance between the object and its image is given by d.

For M < 1, we will have

d = p + q

substituting in q we get:

d = p + -M*p

solving for p we get:

p = d / (1-M)

We can now plug in p and q into the thing lens equation to solve for f:

1/p + 1/q = 1/f

(1-M)/ d + 1/-M*p  = 1/f

solving for f we get:

The steps for solving M>1 is pretty much the same.

only this time you have a converging lens, and the image is still virtual. So we get that

d = -q - p

All the other steps are exactly the same as earlier.  the final solution will be:

answered Apr 10, 2012 by ~Expert~ (3,856 points)
selected Apr 10, 2012 by Gummmys

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