Forming an Image Behind a Convex Mirror

[PeachBanana]

Homework Statement

An object is placed in front of a
convex mirror whose radius of
curvature is R. What is the greatest
distance behind the mirror that an
image can be formed?

A. Infinity
B. R
C. R/2
D. No image can be formed.

Homework Equations

1/do + 1/di = 1/f

The Attempt at a Solution

I'm not sure if I know how to approach this problem. Will you give me a hint to help get started?

 

[AJ Bentley]

you can work out what f is if you know R.

Then try putting the image at each place offered to you as a possibility and work out where the object must be. (Obviously, start with the furthest distance - infinity)

 

[PeachBanana]

Hi.

1 / ∞ + 1 / do = 1 / f

We know 1 / ∞ will go to zero so that leaves us with do = f. Is this answer wrong because we know the object distance can never equal the focal length?

1 / R + 1 / do = 1 / f .

If we know 2f = R, we can substitute.

1 / 2f + 1 / do = 1 / f

2 / 2do = 1 / 2f - 2 / 2f

2 / 2do = -1 / 2f

Is this the correct answer because the focal length is negative?

1 / R / 2 + 1 / do = 1 / f

2R + 1 / do = 1 / f

1 / do = 1 / f - 2R
I'm not sure why this is wrong (if it is).

 

[AJ Bentley]

1/ What makes you say that the object distance can't equal the focal length?

2/ Think about the significance of do being positive or negative - what does that mean?

 

[AJ Bentley]

One more thing.

Is the focal length of a convex mirror positive or negative?

http://www.physicsclassroom.com/class/refln/u13l4d.cfm

 

[PeachBanana]

1. This was an assumption I made I can't support.

2. The sign of do gives a little insight as to what type of mirror is being used. When the object or image is on the reflecting side of the mirror, the corresponding distance is positive. Otherwise, it is negative. Convex mirrors always produce virtual images so do should be positive for a convex mirror.
3. The focal length of convex mirrors are always negative.