A typical diamond is cut as shown in (Figure 1). A ray of light has entered the flat window at the top of the diamond perpendicu
1 answer:
Based on the calculations, the angle relative to the incoming direction is equal to 82°.
<h3>How to calculate the angle?</h3>Based on scientific records and the information provided, we know that the refractive index of diamond is 2.42 and the incident angle (Ia) is 41°.
Next, we would determine the total refraction angle by applying Snell's law:
n₁sini = n₂sinr
2.41sini = 1 × sin90
2.41sini = 1
i = sin⁻¹(1/2.42)
i = 24.41°.
Since Ia is greater than i (41 > 24.41), the ray will pass through the same medium and makes an angle of 41° (normal).
Therefore, the angle relative to the incoming direction is given by:
θ₁ = 41 + 41
θ₁ = 82°.
Read more on refraction here: brainly.com/question/15838784
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Complete Question:
A typical diamond is cut as shown in (Figure 1). A ray of light has entered the flat window at the top of the diamond perpendicular to the surface, as shown in the figure. At what angle relative to the incoming direction is the ray reflected from the first interaction with the surface of the diamond?
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The first and second coordinate points of the sine graph are;
(0, 20) and (2, 22)
<h3>Sine Graph expression</h3>
The general formula we will use to plot the graph is;
y = [Asin (2πx/t)] + ∅ (Note that sin is in radians)
where;
A is amplitude
t is period
∅ is phase shift
We are told that the buoy bobs up and then down 2 meters from the ocean's depth. This means that;
Amplitude; A = 2
Now, Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Thus;
Period = 2 * 4 = 8 seconds
Assume at x = 0, the buoy is at normal ocean depth. Thus;
Phase shift; ∅ = 20
Thus, we have;
y = [2sin((2πx/8)] + 20
At x = 0, we have;
y = [2sin((2π*0/8)] + 20
y = 0 + 20
y = 20
Thus, first point is; (0, 20)
Since the second point must be a maximum or minimum value on the graph closest to the first point, then we put 2 for x to get the coordinate of the second point;
y = [2sin((2π*2/8)] + 20
y = [2sin((2π*2/8)] + 20
y = [2sin(π/2)] + 20
In radians, sin(π/2) = 1. Thus;
y = (2 * 1) + 20
y = 22
Second point is (2, 22)
Using the first and second point coordinates, we will use sine tool to graph the function as attached below.
Read more about sine graph at; brainly.com/question/18055768
