A cup that is 6.0 cm tall is in front of a concave lens.The image of the cup is 2.5 cm tall and 7.5 cm from the lens.What is the focal length of the lens?

Question

Quizplus · Accepted Answer

Using the thin lens equation: 
1/f = 1/d_o + 1/d_i 
Where f is the focal length, d_o is the object distance, and d_i is the image distance. 
Rearranging, we get: 
f = 1/ (1/d_o + 1/d_i) 
Plugging in the given values: 
d_o = -6.0 cm (since the object is in front of the lens) 
d_i = 7.5 cm 
2.5 cm is the height of the image, which means it has a magnification of -2.5/6.0 = -0.42 (negative because it's inverted) 
We know that: 
m = - d_i / d_o 
Rearranging, we get: 
d_o = -d_i / m 
Plugging in the values: 
d_o = 7.5 / 0.42 = 17.9 cm 
Now we can plug in the values to get: 
f = 1/ (1/-6.0 + 1/17.9) = -12.57 cm ≈ -13 cm 
Therefore, the answer is choice C.

A Cup That Is 6