How Do You Calculate the Image Distance and Diameter Using a Spherical Mirror?

[qman]

taking that the sun is 150 million km's away, the keck telescope has a reflective surface with a 5 metre radius of curvature. if the disk of the sun subtends to an angle of 0.5 degree at the earth, adn assuming that the mirror is concae spherically what are the position and diameter of the image of the sun.

so yeah basicall i need a) image distance frlom the mirror
and b) image diameter

please help in any way u can asap as the question is due today :$

 

[Andrew Mason]

taking that the sun is 150 million km's away, the keck telescope has a reflective surface with a 5 metre radius of curvature. if the disk of the sun subtends to an angle of 0.5 degree at the earth, adn assuming that the mirror is concae spherically what are the position and diameter of the image of the sun.

so yeah basicall i need a) image distance frlom the mirror
and b) image diameter

A spherical mirror can be thought of as a thin lens except that the light reflects backward instead of going through it.

The focal length of a spherical mirror is approximately the same as that of a parabola. Work the focal length of a circle $(y+r)^2 + x^2 = r^2$ that is approximately equal to a parabola: $x^2 = 4py$ where p is the focal length of the parabola. The approximation of a parabola to a circle is where y is very small.

Use the thin lens equation to work out the image distance from the object distance and focal length:

$$\frac{1}{O} + \frac{1}{f} = \frac{1}{i}$$

What is the magnification?

AM