Solution Found!
Diffraction effects often involve small angles, and we
Chapter 28, Problem 81GP(choose chapter or problem)
Problem 81GP
Diffraction effects often involve small angles, and we usually make the approximation sin θ ≅ tan θ. To see how accurate this approximation is, complete the following table.
θ(deg) |
θ (rad) |
sin θ |
tan θ |
sin θ/tan θ |
0.0100° |
|
|
|
|
1.00° |
|
|
|
|
5.00° |
|
|
|
|
10.0° |
|
|
|
· |
20.0° |
|
|
|
|
30.0° |
|
|
|
|
40.0° |
|
|
|
|
Questions & Answers
QUESTION:
Problem 81GP
Diffraction effects often involve small angles, and we usually make the approximation sin θ ≅ tan θ. To see how accurate this approximation is, complete the following table.
θ(deg) |
θ (rad) |
sin θ |
tan θ |
sin θ/tan θ |
0.0100° |
|
|
|
|
1.00° |
|
|
|
|
5.00° |
|
|
|
|
10.0° |
|
|
|
· |
20.0° |
|
|
|
|
30.0° |
|
|
|
|
40.0° |
|
|
|
|
ANSWER:
Step 1 of 2
The sine and tangent functions are comparable to each other and to the angle argument as long as the angle is small.
We can convert the angles to radians by multiplying by
