Find the image distance - optical instruments

AI Thread Summary
An object is placed 30 cm in front of a diverging lens with a focal length of 10 cm, prompting a calculation of the image distance using the lens formula. The initial calculation yielded an incorrect image distance of -15 cm due to a miscalculation in the equation. The correct approach involves recognizing that the combined terms should be calculated accurately, leading to the correct image distance of -7.5 cm. It's emphasized that rearranging equations can help predict the sign and magnitude of the result. Accurate calculations are crucial in optics to avoid confusion.
ally1h
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Homework Statement


An object is placed at 30 cm in front of a diverging lens with a focal length of 10 cm. What is the image distance?


Homework Equations


1/f = 1/do + 1/di



The Attempt at a Solution


I thought this was a straight-forward question:
1/di = 1/-f - 1/do
1/di = (1/-10 cm) - (1/30 cm)
1/di = -0.066 cm
di = 1/-0.066 cm = -15 cm

BUT- the answer provided to me states that the answer is -7.5cm. So what is it that I'm missing here?
 
Physics news on Phys.org
Slight calculator typo
(1/-10) - (1/30) = - (1/10 + 1/30) = -0.133
 
Well now... don't I feel silly?

Thank you.
 
It's very easy to get those sort of sums wrong,
It's worth rearranging them so that you know if the answer you expect is +ve or -ve
And in a form where you can estimate the magnitude, eg (1/10+1/30) is obviously going to be a bit bigger than 1/10
 

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