Find the object distances (in terms of f ) for a thinconverging lens of focal le

Question

Find the object distances (in terms of f) for a thinconverging lens of focal length f for the followingconditions: (a) The image is real and the image distance isfive times the focal length.
p = 1f

(b) The image is virtual and the image distance is six times the focal length.
p = 2f

(c) Calculate the magnification of the lens for cases (a) and(b).
In case (a): M = 3
In case (b): M = 4

Not sure how to start the problem. Thank you for yourhelp
(a) The image is real and the image distance isfive times the focal length.
p = 1f

(b) The image is virtual and the image distance is six times the focal length.
p = 2f

(c) Calculate the magnification of the lens for cases (a) and(b).
In case (a): M = 3
In case (b): M = 4

Not sure how to start the problem. Thank you for yourhelp

Explanation / Answer

(a) The image is real and the image distance isfive times the focal length.
p = 1f
magnification = q/p =5f
so q=5pf
we have 1/p+1/q=1/f
1/p=1/f-1/q=1/f-1/5pf=>p=[5f+1]/5
(b) The image is virtual and the image distance is six times the focal length.
p = 2f
magnification = q/p =6f
so q=6pf
we have 1/p-1/q=1/f
1/p=1/f+1/q=1/f+1/6pf=>p=[6f-1]/6

(c) Calculate the magnification of the lens for cases (a) and(b).
In case (a): M = 3=25f/[5f+1]
In case (b): M = 4=36f/[6f-1]

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