Respuesta :
Answer:
D = 2.38 m
Explanation:
This exercise is a diffraction problem where we must be able to separate the license plate numbers, so we must use a criterion to know when two light sources are separated, let's use the Rayleigh criterion, according to this criterion two light sources are separated if The maximum diffraction of a point coincides with the first minimum of the second point, so we can use the diffraction equation for a slit
a sin θ = m λ
Where the first minimum occurs for m = 1, as in these experiments the angle is very small, we can approximate the sine to the angle
θ = λ / a
Also when we use a circular aperture instead of slits, we must use polar coordinates, which introduce a numerical constant
θ = 1.22 λ / D
Where D is the circular tightness
Let's apply this equation to our case
D = 1.22 λ / θ
To calculate the angles let's use trigonometry
tan θ = y / x
θ = tan⁻¹ y / x
θ = tan⁻¹ (4.30 10⁻² / 140 10³)
θ = tan⁻¹ (3.07 10⁻⁷)
θ = 3.07 10⁻⁷ rad
Let's calculate
D = 1.22 600 10⁻⁹ / 3.07 10⁻⁷
D = 2.38 m
Answer:2.38 m
Explanation:
First convert all numbers to meter
4.30 cm ==> 0.43 m=y
140 km ==> 140000m=L
600 nm ==> 6E-7= Wavelength
y=Ltanθ ==>Y/L =tan^-1
Formula θ=1.22*(λ)[tex]theta=\frac{1.22*wavelength{} }{D{} {}{}}[/tex]
[tex]\frac{1.22*(6.0*10^{-7}) }{tan^{-1} (\frac{0.043m}{140000m} )}[/tex]
Plug in the numbers to find the angle
MAKE SURE YOUR CALCULATOR IS IN RADIAN!!!!
You should get 2.38325515m
