Lens and Focal Length Practice Problems

[Suavez]

Homework Statement

A 2.0-cm-diameter spider is 1.80 m from a wall.

A. Determine the focal length of a lens that will make a half-size image of the spider on the wall.

B. Determine the position (measured from the wall) of a lens that will make a half-size image of the spider on the wall.

Homework Equations

(1/p) + (1/q) = (1/f)

m = (-q/p)

The Attempt at a Solution

I couldn't figure out where to start. I understand that the magnification should be (-.05) but then I can't use that equation because I don't know the original focal length. Would 1.80 m be the image distance? I wish the problem would have provided more information!

 

[Redbelly98]

1.80m is not the image distance, it's the distance from the spider to the wall.

And the lens will be somewhere in between the spider and wall.

You can use that information to come up with another equation involving p and q.

p.s. welcome to PF.

 

[Suavez]

1.80m is not the image distance, it's the distance from the spider to the wall.

And the lens will be somewhere in between the spider and wall.

You can use that information to come up with another equation involving p and q.

p.s. welcome to PF.

lol Thanks for welcoming me. The things you stated were the immediate obvious things in my head but I suppose my question should have been, "What is that equation?" The problem says that the distance given is from the spider to the wall. Where to from there?

 

[Redbelly98]

Draw a figure showing the spider, lens, and wall.

Label the distances corresponding to p and q. And indicate the 1.80 m distance also.

The relation should become apparent.

 

[Suavez]

Draw a figure showing the spider, lens, and wall.

Label the distances corresponding to p and q. And indicate the 1.80 m distance also.

The relation should become apparent.

The lens needs to be 0.9 m from the wall? My logic here is 0.5 of the total distance and the magnification is -0.5. If I am correct for this position to produce a half-size image of the spider, what will the focal point have to be for the lens? 0.9 m as well?

 

[Redbelly98]

The lens needs to be 0.9 m from the wall?

No. That would put the lens halfway between the spider and the wall, which means p=q and m=-1.

p+q=____?

 

[Suavez]

No. That would put the lens halfway between the spider and the wall, which means p=q and m=-1.

p+q=____?

Damn, I'm lost. What is the relevence of p+q? My next choice would have been to position the lens 1.35 m away from the from the spider (3/4 of the total distance).

 

[Redbelly98]

Did you draw the figure as I suggested in post #4?

 

[Suavez]

That was the first thing I did for the problem.

 

[Suavez]

I have another problem I'm having some issues with titled "Undefined Angle of Incidence." Any suggestions for that one? I have to submit this take-home exam in 30 minutes and these are the last two problems giving me trouble. I understand things a lot more clearly when I see the broken-down solution and then try another on my own. I'm really lost for these two.