object distance question.. please help :)

Question

A converging lens with f=29.8 cm yields an image with magnification M=−2.5. Find the object distance.
in terms of centimeters. They will be assumed to be cm.
to a precision of tenths of a cm.

 

thank you!!

Answer 1

Use these 2 formulas:

 

(i)   M = -q/p

(ii)  1/q + 1/p = 1/f

 

M = -2.5

q = image distance

p = object distance

f = 29.8 cm

 

We want to solve for p.  First, eliminate q so you are left with one equation in p.

 

M = -q/p ⇒ q = -pM

 

1/p = 1/f - 1/q = 1/f - 1/(-pM) = 1/f + 1/(pM)

 

(1/p)(1 - 1/M) = 1/f

 

p = f(1 - 1/M) = (29.8 cm)[1 - 1/(-2.5)] = 41.72 cm