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Convex mirrors - image size

  • #1
190
0

Homework Statement



Prove that the virtual image in a convex mirror is always smaller than the real object.

Homework Equations



[tex] m = -\frac{d_{i}}{d_{O}}[/tex]

The Attempt at a Solution



Not a hw problem. Something which is bothering me, and haven't been able to prove yet.

Thanks!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
5
When the object is at infinity, where the image is formed in convex mirror. Now write the relation between di, do and f with proper sign. Multiply by di to each term on both the side and find the relation for m. From the result, see whether you get your answer.
 
  • #3
190
0
Thanks for the response.

When the object is at infinity, the image is formed at the focus.

When I multiply both sides by di, I get [tex]-m + 1 = \frac{d_{i}}{f}[/tex]

I still don't see why this proves [tex] |m|< 1 [/tex] :(
 
  • #4
190
0
Ah ok I see it.

[tex]m = 1 - \frac{d_{i}}{f}[/tex]

Since [tex]m = -\frac{d_{i}}{d_{O}}> 0[/tex] for convex mirrors, since the image is behind the mirror, while the object is in front, m is at max 1.

Thanks!
 

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