Question

A two mirror resonator is formed by a convex mirror of radius R1=?1.0 m and a concave mirror of radius R2= 1.5 m. What are the maximum and minimum possible mirror separations, if this is to remain a stable resonator? Draw stable ray configuration for the two marginal cases.

Answer 1

Sol:

Let us consider a resonator (raduis R1 <0) and concave mirror (r2> 0) at a distance d .

The value of d for which the resonator is stable consider both cases |R₁ | > R₂ and |R₁| < R₂

Given Data raduis R1=-1.0m and R2 =1.5m

For Stability , The following formula can be used to find the minimum and maximum possible separations depens on the stable resonator.

Formulae

For Stablity , 0 < (1-d/R1) (1-d/R2) < 1

0< (1-d/-1.0) (1-d/1.5) < 1 -> Equation 1

Let us assume , for value d= 1 ,put in Equaton 1 then

0<(1-1/-1.0) (1-1/1.5) < 1

0 < (1-(-1)) (1-0.666) < 1

0 < (2) (0.334) < 1

0 < 0.668 < 1 - > equation 2

if the value is Negative means it is unstable

Postive Means , it is stable

Hence,The Maximum and Minimum possible mirror separations is remain stable resonator as compare above equation 2 .