- #1
Nabin kalauni
- 26
- 6
Homework Statement
Derive an analytic expression for the distance from the vertex to the focus for a particular ray in terms of (i) the radius of curvature R of the concave mirror (ii) the angle of incidence θ between incident ray and radius of the mirror. Hence show that the focus moves closer to the mirror as rays move towards the outer edge of a concave mirror.
Homework Equations
A. The law of reflection
B. Some basic trigonoteric identities
The Attempt at a Solution
I considered a ray parallel to the optic axis and a height h above the axis. The reflected ray meets the axis at a distance f from the vertex. The sketch is linked to the thread.
I could see pretty easily that θ increases as we take a ray further from the axis. As a result, the point D moves closer to the vertex. But I could not derive a mathematical expression. So I looked at the solution and they used quite a few approximations that baffled me like cos θ = ½R/(R-f). How can we get this identity from the given sketch and what approximations do we use?