Answer:
b) θ = 8.54°, c) θ = 0.955°, d)The sine function cannot be greater than 1. The correct answer is iv)
Explanation:
Diffraction phenomena are described by the equation, for constructive interference
a sin θ = m λ m = ±1, ±2, ±3, ...
Where a is the width of the slit (20 m), λ is the wavelength and m integer
Let's look for the wavelength, for these we use the relationship
c = λ f
λ = c / f
λ = 3 10⁸ / 101 10⁶
λ = 2.97 m
a) Let's look for the angle for the first minimum found in m = 1
θ = sin⁻¹ (m lam / a)
b) Let's calculate
θ = sin⁻¹ (1 2.97 / 20)
θ = sin⁻¹ (0.1485)
θ = 8.54°
c)
λ = 3 10⁸/900 10⁸
λ = 0.333 m
θ = sin⁻¹ (0.333 / 20)
θ = sin⁻¹ (0.166666)
θ = 0.955°
d) repeat the calculations for f = 1000 kHz = 1 MHz
λ = 3 10⁸/1 10⁶
λ = 300 m
θ = sin⁻¹ (300/20)
θ = sin⁻¹ (15)
The sine function cannot be greater than 1.
The correct answer is iv)
