Answer:
a) θ = λ / a , b) θ = 0.294 rad , c) θ = 0.0333 rad , d) correct answer is IV
Explanation:
a) The equation that describes the diffraction process is
a sin θ = m λ
Where a is the slit size, λ is the wavelength and m is an integer
In our case the firtz minimum occurs for m = 1
a sin θ = λ
In general in the direction problems the angles are very small, we can approximate the sine function
sin θ = θ
a θ = λ
θ = λ / a
To give a number we must have a specific separation of the buildings, suppose the separation given by the width of a street 10 m with value for a (a = 10m)
b) the speed of light is related to wavelength and frequency
c = λ f
λ = c / f
λ = 3 10⁸/102 10⁶
λ = 2.94 m
θ = 2.94 / a
The angle is in radians, to observe the phenomenon depends the separation of the building, in general the maximum value of a = 2.94 m
The angle for a = 10m
θ = 0.294 rad
c) let's look for the wavelength
λ = 3 10⁸/900 10⁶
λ = 0.333 m
θ = 0.333 / a
For a = 10m
θ = 0.0333 rad
d) f = 1000 kHz = 1 10⁶ MHz this case
λ = 3 10⁸⁸/1 10⁶
λ = 3 10² m
θ = 300 / a
For a = 10 m
θ = 300/10
θ = 30
For this number, the originate sine function would give a value greater than 1, so it is not defined
The correct answer is IV
