In the figure,the image is viewed on a screen and is 13.5 mm tall.What is the focal length of the lens?
A)+14.6 cm
B)-14.6 cm
C)+20.4 cm
D)-89.3 cm
E)+124 cm

Question

In the figure,the image is viewed on a screen and is 13.5 mm tall.What is the focal length of the lens? 
A)+14.6 cm 
B)-14.6 cm 
C)+20.4 cm 
D)-89.3 cm 
E)+124 cm

Quizplus · Accepted Answer

Using the thin lens equation, where f is the focal length, d_i is the object distance and d_o is the image distance:
1/f = 1/d_i + 1/d_o
As the image is viewed on a screen, the image distance can be considered essentially infinite. 
Therefore, 1/f = 1/d_i
Rearranging, d_i = f
Using similar triangles, we can write:
d_i / h_i = d_o / h_o
As the image height, h_i, is given as 13.5 mm and the object distance, d_i, is equal to the focal length, f, we can write:
f / 13.5 mm = d_o / h_o
Using the given values of h_o and f, we can solve for d_o:
d_o = f * h_o / h_i
Substituting the given values, we get:
d_o = f * 250 mm / 35 mm
Thus, d_o = 7.14f mm
As the image is formed behind the lens (inverted), the object distance, d_i, is negative. Therefore, f = -d_i.
Substituting, we get:
d_o = -7.14d_i
As d_i and d_o are both negative, we can drop the negative signs:
7.14d_i = d_o
Substituting the value of d_o, we get:
7.14d_i = f * 250 mm / 35 mm
Simplifying, we get:
d_i = f * 20.4 mm
Substituting the given value of h_i, we get:
f / 13.5 mm = 1 / (f * 20.4 mm)
Solving for f, we get:
f = 20.4 cm
Therefore, the focal length of the lens is +20.4 cm.

In the Figure,the Image Is Viewed on a Screen and Is