Optics Problem: Trouble Visualizing it

[justadream]

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Can someone show and/or explain how to do this problem:

“If a certain eye can only focus on objects at least 50cm away, which of the following lenses, if placed in front of the eye, would allow it to focus on an object 25 cm away??



Answer: A converging lens with a focal length 50 cm.

 

[Cawolf]

Sure. It is just using the thin lens equation.

f = (1/do + 1/di)^-1

We know the object is at 25cm and the image is desired to be at 50cm - but it front of the lens so it is negative.

f = (1/25 -1/50)^-1

=(1/50)^-1

f=50cm

Also I am not sure what the choices are - but by seeing this person is hyperopic, you should know to use a converging lens.

 

[justadream]

@Cawolf

My main problem with the question was knowing to make it "-50" instead of "50".

How do you know the image distance is negative? I'm having trouble visualizing the placement of the image relative to the lens.

 

[Cawolf]

Well, think about the statement.

It says that they have a near point of 50 cm, so we want the image to be there.

The object distance is given.

The image has to be in front of the lens - making the distance negative.

I will try a sketch.

 

[Cawolf]

It is convention that you call an image on the same side as the object negative.

This is how reading glasses work. You place an image inside the focal length of a converging lens and it produces a magnified, erect, virtual image farther away - so the hyperopic person can see it clearly.