How Do Radiowaves Interfere Destructively at a Cliffside Radiotelescope?

[EmmaK]

Homework Statement

A radiotelescope is positioned at a height of h=150m on a cliff overlooking the sea. A very distant galaxy emitting radiowaves, wavelength 3m, is at an angle $$\theta$$ above the horizion. The radiowaves reach the telescope both directly and after reflection off the water surface. Show that if $$\theta$$=57degrees, then the 2 rays interfere destructively, so that the signal received is zero. Note that the refractive index,n,of the sea is greater than that of air

Homework Equations

dsin$$\theta$$=(m+1/2)$$\lambda$$ for destructive interference.

The Attempt at a Solution

Tried substituting the values into the equation, with d=2hsin$$\theta$$, and expected to get m as an integer, but didnt..

 

[EmmaK]

anyone?

 

[ideasrule]

Homework Statement

A radiotelescope is positioned at a height of h=150m on a cliff overlooking the sea. A very distant galaxy emitting radiowaves, wavelength 3m, is at an angle $$\theta$$ above the horizion. The radiowaves reach the telescope both directly and after reflection off the water surface. Show that if $$\theta$$=57degrees, then the 2 rays interfere destructively, so that the signal received is zero. Note that the refractive index,n,of the sea is greater than that of air

Homework Equations

dsin$$\theta$$=(m+1/2)$$\lambda$$ for destructive interference.

The Attempt at a Solution

Tried substituting the values into the equation, with d=2hsin$$\theta$$, and expected to get m as an integer, but didnt..

That equation doesn't apply here; I'll leave it to you to figure out why. You have to approach this problem from first principles. First, calculate the path length difference between the reflected ray and the direct ray.

 

[EmmaK]

oh ok, is the path difference not 2hsin(theta)=300sin(theta) either?

 

[ideasrule]

I see no obvious reason why it should be equal to that.

 

[EmmaK]

ok.. i just used trig. sin(angle) = opposite/hypotenuse. want to find hypotenuse and opposite =h. and there's 2 of these triangles, so path difference is double this..hard to explain without a diagram!

 

[Stonebridge]

I have given you a hint (with diagram) on the TSR physics site.