MHB What Are the Properties of Concave/Convex Spherical Mirrors?

Click For Summary
Concave spherical mirrors have specific properties that can be calculated using formulas. For a concave mirror with a focal length (f) of 12 cm and an object distance (p) of 18 cm, the radius of curvature (r) is determined to be 24 cm. The image distance (i) is calculated as 36 cm, and the magnification (m) is found to be -2. The image produced by the concave mirror is real and inverted, indicating that it is not imaginary. Understanding these properties is essential for applications in optics and physics.
mglander
Messages
1
Reaction score
0
Spherical mirrors. We are given p= +18 and the mirror is concave with f= 12. Find r, i, m, Real or Virtual, Imaginary or not imaginary, and what side of the mirror is the image on. All units are cm.

r: f=r/2, so r=2f r= 24 cm
i: (1/p) + (1/i)= (1/f), so (1/f)-(1/p)=(1/i) i= 36 cm
m: m=-i/p m=-2

At that point, how do you know whether the image is Real or Virtual and Imaginary or Not Imaginary?
 
Mathematics news on Phys.org
Thread 'Erroneously  finding discrepancy in transpose rule'
Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
Replies
11
Views
2K
Replies
19
Views
904
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 172 ·
6
Replies
172
Views
20K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 11 ·
Replies
11
Views
1K
Replies
7
Views
2K