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

In summary, the size of the image formed by a concave mirror is proportional to R^n where R is the radius of curvature. The value of n is 1 when the object is at an infinite position. The equation for magnification is given by k(R^n) / size of object, where n needs to be the least for the magnification to be very small.
  • #1
DriggyBoy
19
0
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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  • #2
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.
 
  • #3
Ok thnx...but what if the object is at infinite position??
...btw answer given in the book is 1
n=1
 
  • #4
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:
  • #5
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 ?
 
  • #6
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?
 
  • #7
DriggyBoy said:
Cannot proceed... 1/v + 1/u = R/2

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

1. What is the formula for determining the relationship between the radius of curvature and the power of a concave mirror?

The formula is n = -2R, where n is the power of the mirror and R is the radius of curvature.

2. How does the power of a concave mirror affect the size of the reflected image?

The power of a concave mirror, represented by n, is directly proportional to the size of the reflected image. This means that as the power increases, the size of the image also increases.

3. How do I find the value of n for a specific concave mirror?

To find the value of n for a concave mirror, you need to know the radius of curvature. Once you have this value, you can plug it into the formula n = -2R and solve for n.

4. Can the value of n be negative for a concave mirror?

Yes, the value of n can be negative for a concave mirror. This indicates that the image is inverted and magnified.

5. How does the value of n change when the distance between the object and the mirror is changed?

The value of n remains constant when the distance between the object and the mirror is changed. This means that the power of the mirror will not change, but the size and location of the reflected image will be affected.

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