Find the image distance - optical instruments

In summary, the conversation discusses an object placed in front of a diverging lens with a focal length of 10 cm and the resulting image distance. The original solution was incorrect due to a calculator typo, resulting in a negative answer of -15 cm. The correct answer is -7.5 cm, which was provided by another person in the conversation. It is suggested to rearrange equations and estimate the magnitude of answers to avoid simple errors.
  • #1
ally1h
61
0

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?
 
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  • #2
Slight calculator typo
(1/-10) - (1/30) = - (1/10 + 1/30) = -0.133
 
  • #3
Well now... don't I feel silly?

Thank you.
 
  • #4
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
 

FAQ: Find the image distance - optical instruments

What is an optical instrument?

An optical instrument is a device that uses light to magnify, view, or analyze objects. Examples include microscopes, telescopes, and cameras.

How does an optical instrument work?

Optical instruments use lenses, mirrors, and other components to manipulate light in order to produce an image of an object. The light enters the instrument, is refracted or reflected by the lenses and mirrors, and forms an image that can be viewed or captured.

How do you find the image distance in an optical instrument?

The image distance in an optical instrument can be found by using the thin lens equation, which states that the image distance (di) equals the product of the object distance (do) and the focal length (f), divided by the difference between the focal length and the object distance (f-do). This can also be calculated using the magnification equation, which states that the magnification (M) equals the ratio of the image distance to the object distance.

What factors affect the image distance in an optical instrument?

The image distance in an optical instrument can be affected by the focal length of the lenses or mirrors, the distance between the lenses or mirrors, and the type of instrument being used. Additionally, the refractive index of the material used for the lenses or mirrors can also affect the image distance.

How can the image distance be adjusted in an optical instrument?

The image distance in an optical instrument can be adjusted by changing the focal length of the lenses or mirrors, adjusting the distance between the lenses or mirrors, or by using different lenses or mirrors with varying refractive indices. Additionally, the position and focus of the object being viewed or captured can also affect the image distance.

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