equation is: n1sino1=n2sino2
(o means theta)
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Given info:
So n1=1.5 n2=1.0
o1(incident angle)=20
solve for o2
Can you check this:
n1sin20=n2sino2
1.5x0342=1sino2
.513=sino2
inverse sin(.513)
o2=30.86 degrees
is this right?
N1 sin A1 = N2 sin A2
1.5 sin 20 = 1 sin A2
1.5 sin 20 = .513
sin^-1 .513 = 30.8 yes
thanks for the check!
To solve for θ2 (o2), we have the equation:
n1 * sin(θ1) = n2 * sin(θ2)
Given information:
n1 = 1.5
n2 = 1.0
θ1 = 20°
Substituting these values into the equation, we have:
1.5 * sin(20°) = 1.0 * sin(θ2)
Now, let's solve for sin(θ2):
sin(θ2) = (1.5 * sin(20°)) / 1.0
sin(θ2) = 1.5 * sin(20°)
Using a calculator, we find:
sin(θ2) ≈ 0.513
Next, we need to find the inverse sine (sin^(-1)) of 0.513 to get θ2.
Using a calculator or a trigonometric table, we find:
θ2 ≈ 30.86°
So, your answer of θ2 = 30.86 degrees is correct!
To verify the solution, let's go through the steps and calculations together.
The given equation is n1sin(o1) = n2sin(o2), where n1 = 1.5, n2 = 1.0, and o1 = 20 degrees. We need to solve for o2.
Step 1: Substitute the given values into the equation:
1.5sin(20) = 1.0sin(o2)
Step 2: Calculate the left side of the equation:
1.5 x sin(20) ≈ 0.5147
Step 3: Rewrite the equation using this result:
0.5147 = 1.0sin(o2)
Step 4: Solve for o2:
Divide both sides of the equation by 1.0:
sin(o2) = 0.5147 / 1.0 ≈ 0.5147
Step 5: Calculate the inverse sine of 0.5147 to find o2:
o2 ≈ sin^(-1)(0.5147) ≈ 30.86 degrees
So, your solution is correct. The value of o2 is approximately 30.86 degrees.