Finding the exponent n in image size proportional to R^n for concave mirrors

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The size of image formed by a concave mirror is proportional to R^n where R is radius of curvature. Find n.
Cannot understand how to proceed. Need help.
 
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It's not. The size of the image is a function of R and the distance between the object and the mirror. Even for a fixed object distance the size of the image is a function of R but not proportional to R.
 
Ok thnx...but what if the object is at infinite position??
...btw answer given in the book is 1
n=1
 
DriggyBoy said:
Ok thnx...but what if the object is at infinite position??
...btw answer given in the book is 1
n=1

That's right. For the object distance >> R the answer is proportional to R1. But not R = ∞ since then the image size is zero unless it's also infinite in size!

So, to continue:

1. what is the simple equation relating object o and image i distances, and the radius R?
2. what is the expression for magnification?
3. what is #2 when o >> R?
 
Last edited:
Cannot proceed... 1/v + 1/u = R/2
Now can we omit 1/u cause its too small?
Then eqn bcums v=2/R...from this it is clear that image is at focus
Now what ?
 
Btw i think i proceeded a bit further...Now magnification is very small...
Now size of image/size of object = magnification(very small)
or, size of image = magnification * size of object
or, k(R^n) = magn * size of objct
or, magn = { k(R^n) } / Size of objct
This magn is very small, for it to be very small, n needs to be least...therefore n = 1
Is that it?