Calculate the frequency of microwave

[patrykh18]

Homework Statement

Two single frequency coherent microwave beams are directed from the same point towards a concave mirror. One beam is incident parallel to the principal axis of the mirror, 0.06m from the axis. The other beam passes through the focal point before striking the mirror. The strongest possible signal that can be produced by the combination of the two beams is detected where they meet, 0.3m away from the mirror. f=0.2m

Calculate:
1) how far from the mirror do the two beams originate
2) how far below the axis do they meet
3) minimum possible frequency of the microwaves

c= 3x10^8 m/s

Homework Equations

1/f= 1/u + 1/v
m=v/u
c=fλ

The Attempt at a Solution

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1) In this question I used the 1/f= 1/u +1/v formula.
I got the answer of 0.6m

2) In this case I used the m= v/u formula. Knowing that the size of the object is 0.06m (or rather its 0.06m away form principal axis) I got the answer of 0.03m

3) Not 100% sure about this one although first I found the distance from f to the source. I used trigonometry to find the hypotenuse. I got a triangle of lengths 0.06m, 0.4m, and 0.404m. I figured that the 0.404m side is 1 wavelength longer than the 0.4m side. So I found wavelength of the wave. Then I used the last formula and I found the answer to be around 7.5x10^10 Hz. Could somebody tell me whether I am right or wrong because I have no access to the solution.

 

[Simon Bridge]

Your reasoning is sound - the first two are geometric optics questions, for the last one - did you account for a phase shift on reflection?

Note: for the 1st two you are approximating whatever the undisclosed concave mirror shape was by a thin parabolic mirror for the equation to work. You are also assuming that 6mm is close enough to the optic axis for the par-axial approximation to be valid. Technically you are not given enough information - but it is probably reasonable to do this in context of your course.