The focal length of a converging lens that projects the image of a lamp,magnified 4 times,onto a screen 3.05 m from the lamp is approximately
A)11.6 cm
B)48.8 cm
C)-11.6 cm
D)2.04 m
E)19.2 cm

Question

Quizplus · Accepted Answer

We can use the magnification equation, which relates the image distance (di), object distance (do), and magnification (m) to the focal length (f): 
m = -di/do = f/(do-f)
In this problem, we are given that the magnification is 4, the object distance is not specified, and the image distance (di) is the distance from the lens to the screen, which is 3.05 m. 
So, we can rearrange the magnification equation to solve for f: 
f = m*do/(1+m)*di 
Plugging in the given values, we get: 
f = 4*do/(1+4)*3.05 = 0.488*do 
Since we don't know the object distance, we can't get a numerical answer for f. However, we can see that f is directly proportional to do, which means it will increase if the object is moved further away from the lens. Therefore, the only answer choice that makes sense is B, 48.8 cm, which is the largest option and corresponds to a relatively distant object.

The Focal Length of a Converging Lens That Projects the Image