A problem regarding the lens formula

[jxocq]

Homework Statement

An arrow of 2cm length stands about 6cm away from a convex lens (f = 2cm). How long is the image of the arrow?

Homework Equations

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The Attempt at a Solution

Whenever I get homework regarding optics and particularly the lens formula, I never really know where to start. I tried filling the numbers I've been given into the formula but I'm really unsure if I'm doing the right thing and if all the numb are entered in the correct places.

 

[ZapperZ]

First, write down the lens equation here, and tell us if you know what the symbols mean.

Zz.

 

[jxocq]

First, write down the lens equation here, and tell us if you know what the symbols mean.

Zz.

1/V - 1/U = 1/F is the formula right?
Where V is the distance of the image from the centre of the lens, U is the distance of the object of the centre of the lens and F is the focal length of the lens.

 

[ZapperZ]

1/V - 1/U = 1/F is the formula right?
Where V is the distance of the image from the centre of the lens, U is the distance of the object of the centre of the lens and F is the focal length of the lens.

Are you sure about the minus sign?

Zz.

 

[jxocq]

Are you sure about the minus sign?

Zz.

Yikes. I went to look on the internet now and different sources say multiple things. Maybe because it's a convex lens it should be 1/F = 1/V + 1/U ?

 

[ZapperZ]

Yikes. I went to look on the internet now and different sources say multiple things. Maybe because it's a convex lens it should be 1/F = 1/V + 1/U ?

Where did you get the minus sign in the first place? It has nothing to do with whether it is convex or concave.

Next, draw a picture and show in the sketch the distance representing V and U.

Zz.

 

[robphy]

Learn to draw ray diagrams.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html
https://www.geogebra.org/m/KYNsUZXH
Due to various sign conventions, I find it difficult to just rely on formulas.
But with a ray diagram... i can see the physics better.
Then use that diagram to clarify the definitions in your formulas.

 

[jxocq]

Where did you get the minus sign in the first place? It has nothing to do with whether it is convex or concave.

Next, draw a picture and show in the sketch the distance representing V and U.

Zz.

I'm not sure but something like this?

 

[nrqed]

Homework Statement

An arrow of 2cm length stands about 6cm away from a convex lens (f = 2cm). How long is the image of the arrow?

Homework Equations

-

The Attempt at a Solution

Whenever I get homework regarding optics and particularly the lens formula, I never really know where to start. I tried filling the numbers I've been given into the formula but I'm really unsure if I'm doing the right thing and if all the numb are entered in the correct places.

Note that for a convex lens, f is taken negative, so in the formula you should use f=-2 cm

 

[robphy]

When drawing ray diagram, use as much space as you can... and use a straightedge.
The horizontal scale and vertical scale can be different.
What will also be important is to draw the lens plane and the lens' focal points.

 

[jxocq]

Learn to draw ray diagrams.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html
https://www.geogebra.org/m/KYNsUZXH
Due to various sign conventions, I find it difficult to just rely on formulas.
But with a ray diagram... i can see the physics better.
Then use that diagram to clarify the definitions in your formulas.

They do look kinda daunting but I'll be sure to learn to get better with them. I did a few assignments with them but i never really understand what I'm doing when I have to use them

 

[ZapperZ]

I'm not sure but something like this?

You don't appear to understand what you either read, or wrote. You earlier wrote:

V is the distance of the image from the centre of the lens

Does this match your sketch?

What is puzzling me here is that it is as if you either don't have a textbook, or you never took any class notes. Why is this the case?

Even if that were the case, if you had done a search on "lens equation", you would have seen, for example, the hyperphysics site. This page clearly indicates what the lens equation means, and how to use it. So I am not sure why you are having a problem with this. I'm trying to figure out the source of the problem here.

Zz.

 

[jxocq]

You don't appear to understand what you either read, or wrote. You earlier wrote:
Does this match your sketch?

What is puzzling me here is that it is as if you either don't have a textbook, or you never took any class notes. Why is this the case?

Even if that were the case, if you had done a search on "lens equation", you would have seen, for example, the hyperphysics site. This page clearly indicates what the lens equation means, and how to use it. So I am not sure why you are having a problem with this. I'm trying to figure out the source of the problem here.

Zz.

I'm homeschooled (It's a Dutch online school) so I do have a textbook and do make my homework, but I basically have to figure everything out by myself. I've mailed my teacher for explanation but their Christmas break has already started so I resorted to here. I just can't wrap my head around the lens formula

 

[PKM]

In the thin lens formula ##\frac {1}{f}=\frac {1}{v}-\frac {1}{u}##, as you've already mentioned, ##u## & ##v## are distances of obj. & img. resp. from the center of the lens. Check that in your diagram you've marked the height of the arrow as ##v##.