EK #957 Physics 1001

[mtravis2190]

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Hi there everyone!

I've been working on question 957 from EK. For most part it makes sense, but I'm not entirely sure. The question goes as follows...

Q. 957- In a flashlight, a concave mirror is used to create a beam of light with parallel rays. Where should the light be placed?
a. at the focal point of the mirror
b. at twice the focal distance of the mirror
c. at the half the focal distance from the mirror
d. at the radius of curvature of the mirror

Answer is a. at the focal point of the mirror.

I keep thinking it should be at twice the focal distance. I'm pretty bad with optics. If anyone can justify this answer for me, I would really appreciate that!

 

[Cmdr_Shepard]

Try to think of a concave mirror like a convex lens, and a convex mirror like a concave lens. A lot of the equations and positions of the various images and objects and focal lengths make more sense that way.

In other words, write out the four different possibilities for lenses and mirrors and see if you can spot the similarities in the equations for each scenario. For your question, it's kinda like a convex lens where light is coming from infinity and being focused at the focal point on the other side of the lens, except it's just on the same side, and the source is at the focal point instead of the image.

You need to be able to see patterns in the void to do well on the MCAT.

 

[brood910]

You have to know the ray diagrams for converging + diverging mirrors and lens.
They are pretty simple. In short, for converging lens/mirror, parallel rays come from rays that go through the focal point.

If you want to know basic rules in a concise way, here it is:

Diverging lenses + mirrors:
- ALWAYS upright, virtual, smaller

Converging lenses + mirrors:
- When o > f, it's real, inverted.
=> Larger if R (2f) > o
=> Smaller if R < o
=> Same if R = o

- When f > o, it's virtual, upright, larger.

Also, note that f is + for converging and - for diverging for both mirrors and lenses

If you memorize this, optics will be a piece of cake for you.
But, you must be able to use equations like 1/f = 1/o + 1/i to do well on optics as well.

 

[mtravis2190]

You have to know the ray diagrams for converging + diverging mirrors and lens.
They are pretty simple. In short, for converging lens/mirror, parallel rays come from rays that go through the focal point.

If you want to know basic rules in a concise way, here it is:

Diverging lenses + mirrors:
- ALWAYS upright, virtual, smaller

Converging lenses + mirrors:
- When o > f, it's real, inverted.
=> Larger if R (2f) > o
=> Smaller if R < o
=> Same if R = o

- When f > o, it's virtual, upright, larger.

Also, note that f is + for converging and - for diverging for both mirrors and lenses

If you memorize this, optics will be a piece of cake for you.
But, you must be able to use equations like 1/f = 1/o + 1/i to do well on optics as well.

Thank you so much! I did several EK questions after this question that I posted and I think I have most of the parameters memorized now! Your list definitely helped to reaffirm things. However, I have one question about diverging lenses (concave lens). Does it only form an image when the object is within one focal length? I saw this statement as an explanation to question 987. I've referred back to physicsclassroom.com and don't see anything like it there. Could you tell me if this rule is in fact true?
Thanks, again!

 

[mtravis2190]

You have to know the ray diagrams for converging + diverging mirrors and lens.
They are pretty simple. In short, for converging lens/mirror, parallel rays come from rays that go through the focal point.

If you want to know basic rules in a concise way, here it is:

Diverging lenses + mirrors:
- ALWAYS upright, virtual, smaller

Converging lenses + mirrors:
- When o > f, it's real, inverted.
=> Larger if R (2f) > o
=> Smaller if R < o
=> Same if R = o

- When f > o, it's virtual, upright, larger.

Also, note that f is + for converging and - for diverging for both mirrors and lenses

If you memorize this, optics will be a piece of cake for you.
But, you must be able to use equations like 1/f = 1/o + 1/i to do well on optics as well.

Also can you please clarify what R stands for? I've seen two different meanings for it while studying through different sets of books.
Thanks

 

[mtravis2190]

Nvm...just re-read your post. R is 2f.