Optics: Find n for Proportionality of Concave Mirror Image to R^n

[DriggyBoy]

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.

 

[rude man]

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.

 

[DriggyBoy]

Ok thnx...but what if the object is at infinite position??
...btw answer given in the book is 1
n=1

 

[rude man]

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?

 

[DriggyBoy]

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 ?

 

[DriggyBoy]

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?

 

[rude man]

Cannot proceed... 1/v + 1/u = R/2

Your equation is dimensionally incorrect. Which means it is incorrect. Fix it!