What is the image distance of an object placed at a distance of 2f from a converging lens of focal length f?

matilda_xc

4 years ago

1/v = 1/f - 1/2f
v = (2f x f)/(2f-f)
v = 2f^2/f
v = 2f

mosunmolaishola

2 years ago

¹/f=¹/u+¹/v
But u=2f
Substituting it into the equation, we have

¹/f=¹/2f+¹/v
¹/v=¹/f–¹/2f
¹/v=(2-1)/2f (LCM)
¹/v=¹/2f

Cross multiplying
V=2f

12Lordz

1 year ago

To solve this, we'll use the *lens formula*:


1/f = 1/v - 1/u


Where:
- f is the focal length (positive for converging lenses)
- u is the object distance (always negative in lens formula conventions)
- v is the image distance

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Given:
- Focal length f
- Object distance u = -2f (since object is placed *2f* in front of the lens)

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Plug into the lens formula:


1/f = 1/v - 1/-2f⇒1/f = 1/v + 1/2f



⇒1/v = 1/f - 1/2f = 1/2f



⇒ v = 2f


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Final Answer:

2f


The image is formed on the *opposite side* of the lens, real and same size as the object.