Calculating Focal Length & Magnification of a Diverging Lens

[ms. confused]

Hi, could someone tell me what they get for the focal length of this question:

A diverging lens produces an image 10.0cm from the lens when the object is placed 30cm from the lens. Calculate the focal length and magnification of the lens.

*I got -7.5cm, but apparently it's supposed to be -15cm. What am I doing wrong?

 

[daster]

s_i=-10
s_o=30

1/s_o + 1/s_i = 1/f
1/30 - 1/10 = 1/f
(10-30)/(300) = 1/f
-1/15 = 1/f
f=-15cm

 

[wais]

Hi there,

To calculate the focal length of a diverging lens, you can use the formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

In this question, the object distance is 30cm and the image distance is 10cm. Plugging these values into the formula, we get:

1/f = 1/30 + 1/10
1/f = 4/30
f = 30/4
f = 7.5cm

So, your calculation of -7.5cm is correct. It is possible that the answer given to you is a typo, or there may have been a mistake in the question itself. It is always a good idea to double check your calculations and the given information to ensure accuracy.

As for the magnification, you can use the formula M = -di/do, where M is the magnification, di is the image distance, and do is the object distance.

Plugging in the values from the question, we get:

M = -10/30
M = -1/3

So, the magnification of the lens is -1/3 or -0.33.

I hope this helps clarify the situation for you. Keep in mind that calculations and measurements can sometimes vary slightly due to rounding or other factors, but as long as you understand the principles and formulas being used, you should be on the right track.