In the experiment, we will be using Snell's law to measure the index of refraction of a material. The incident angle 8, and refraction angle 82 are related by n₁ sin 0₁ = n₂ sin 0₂. Since the angles are measured with uncertainties, the sine of the angles also have uncertainty. The following exercise should help you to get familiar with the uncertainty calculations in this lab. If 0+50=30°± 0.5°, convert 0 into radians. 30° = 0.5⁰ = rad. rad. Calculate the value of sin 8 using degree and radians. sin = You should get the same value for sin if is in radians.
In the experiment, we will be using Snell's law to measure the index of refraction of a material. The incident angle 8, and refraction angle 82 are related by n₁ sin 0₁ = n₂ sin 0₂. Since the angles are measured with uncertainties, the sine of the angles also have uncertainty. The following exercise should help you to get familiar with the uncertainty calculations in this lab. If 0+50=30°± 0.5°, convert 0 into radians. 30° = 0.5⁰ = rad. rad. Calculate the value of sin 8 using degree and radians. sin = You should get the same value for sin if is in radians.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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need help with this, thank you
![**Pre-lab: Refraction with Ray Table and Plastic Block**
In this experiment, we will use Snell’s law to measure the index of refraction of a material. The incident angle \( \theta_1 \) and refraction angle \( \theta_2 \) are related by \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \). Since the angles are measured with uncertainties, the sine of the angles also have uncertainty.
The following exercise should help you get familiar with the uncertainty calculations in this lab.
**If \(\theta \pm \delta \theta = 30^\circ \pm 0.5^\circ\), convert \(\theta\) into radians.**
\[ 30^\circ = \_\_\_\_\_\_\_\_\_\_\ \text{rad.} \]
\[ 0.5^\circ = \_\_\_\_\_\_\_\_\_\_\ \text{rad.} \]
Calculate the value of \(\sin \theta\) using degrees and radians.
\[ \sin \theta = \_\_\_\_\_\_\_\_\_\_\_\_ \]
You should get the same value for \(\sin \theta\) if \(\theta\) is in radians.
Refer to the lab manual G-7 to calculate the uncertainty in \(\sin \theta\).
\[ \frac{\delta (\sin \theta)}{\sin \theta} = \]
\[ \delta (\sin \theta) = \]
We usually refer to the side where the ray is incident on the boundary as medium 1, and the side where the ray is refracted as medium 2. If the index of refraction of medium 2 is smaller than that of medium 1, total internal reflection could happen. The critical angle is \(\theta_c\), where \(\sin \theta_c = \frac{n_2}{n_1}\). If \(n_2\) is known, then the index of refraction of the incident side can be calculated using the critical angle \(\theta_c\).
If \(n_2 = 1.00\) and \(\theta_c = 40^\circ \pm 1^\circ\), calculate the value of \(n_1\) and its uncertainty.
\[ n_1 = \_\_\_\_\_\_\_\_\_\_\_\_ \]
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77d2f4c8-4183-4052-877b-b5f84c5df55f%2Fed76609c-0985-4d2a-b656-725f619e716c%2F84perzb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Pre-lab: Refraction with Ray Table and Plastic Block**
In this experiment, we will use Snell’s law to measure the index of refraction of a material. The incident angle \( \theta_1 \) and refraction angle \( \theta_2 \) are related by \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \). Since the angles are measured with uncertainties, the sine of the angles also have uncertainty.
The following exercise should help you get familiar with the uncertainty calculations in this lab.
**If \(\theta \pm \delta \theta = 30^\circ \pm 0.5^\circ\), convert \(\theta\) into radians.**
\[ 30^\circ = \_\_\_\_\_\_\_\_\_\_\ \text{rad.} \]
\[ 0.5^\circ = \_\_\_\_\_\_\_\_\_\_\ \text{rad.} \]
Calculate the value of \(\sin \theta\) using degrees and radians.
\[ \sin \theta = \_\_\_\_\_\_\_\_\_\_\_\_ \]
You should get the same value for \(\sin \theta\) if \(\theta\) is in radians.
Refer to the lab manual G-7 to calculate the uncertainty in \(\sin \theta\).
\[ \frac{\delta (\sin \theta)}{\sin \theta} = \]
\[ \delta (\sin \theta) = \]
We usually refer to the side where the ray is incident on the boundary as medium 1, and the side where the ray is refracted as medium 2. If the index of refraction of medium 2 is smaller than that of medium 1, total internal reflection could happen. The critical angle is \(\theta_c\), where \(\sin \theta_c = \frac{n_2}{n_1}\). If \(n_2\) is known, then the index of refraction of the incident side can be calculated using the critical angle \(\theta_c\).
If \(n_2 = 1.00\) and \(\theta_c = 40^\circ \pm 1^\circ\), calculate the value of \(n_1\) and its uncertainty.
\[ n_1 = \_\_\_\_\_\_\_\_\_\_\_\_ \]
\[
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need the bottom part for n1 and difference of n1, thank you, show work please.
![**Pre-lab: Refraction with Ray Table and Plastic Block**
In this experiment, we will use Snell’s law to measure the index of refraction of a material. The incident angle \( \theta_1 \) and refraction angle \( \theta_2 \) are related by:
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]
Since the angles are measured with uncertainties, the sine of the angles also have uncertainty.
**Exercise for Familiarity with Uncertainty Calculations:**
If \( \theta \pm \delta \theta = 30^\circ \pm 0.5^\circ \), convert \( \theta \) into radians.
- \( 30^\circ = \underline{\hspace{80px}} \) rad.
- \( 0.5^\circ = \underline{\hspace{80px}} \) rad.
**Calculate the value of \( \sin \theta \) using degree and radians.**
- \( \sin \theta = \underline{\hspace{80px}} \)
You should get the same value for \( \sin \theta \) if \( \theta \) is in radians.
**Refer to the lab manual G-7 to calculate the uncertainty in \( \sin \theta \).**
- \(\delta (\sin \theta)/\sin \theta =\)
- \(\delta (\sin \theta) =\)
**Additional Notes:**
The side where the ray incident on the boundary is referred to as medium 1, and the side with the refracted ray as medium 2. If the index of refraction of medium 2 is smaller than that of medium 1, total internal reflection could occur. The critical angle \( \theta_c \) is given by:
\[ \sin \theta_c = n_2/n_1 \]
If \( n_2 \) is known, the index of refraction of the incident side can be calculated using \( \theta_c \). If \( n_2 = 1.00 \) and \( \theta_c = 40^\circ \pm 1^\circ \), calculate the value of \( n_1 \) and its uncertainty.
- \( n_1 = \underline{\hspace{150px}} \)
- \( \delta n_1 = \underline{\hspace{150px}} \)](https://content.bartleby.com/qna-images/question/77d2f4c8-4183-4052-877b-b5f84c5df55f/f2b36f16-0f87-491d-b3be-0a4147d0f8ca/gnrv7o6_processed.jpeg)
Transcribed Image Text:**Pre-lab: Refraction with Ray Table and Plastic Block**
In this experiment, we will use Snell’s law to measure the index of refraction of a material. The incident angle \( \theta_1 \) and refraction angle \( \theta_2 \) are related by:
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]
Since the angles are measured with uncertainties, the sine of the angles also have uncertainty.
**Exercise for Familiarity with Uncertainty Calculations:**
If \( \theta \pm \delta \theta = 30^\circ \pm 0.5^\circ \), convert \( \theta \) into radians.
- \( 30^\circ = \underline{\hspace{80px}} \) rad.
- \( 0.5^\circ = \underline{\hspace{80px}} \) rad.
**Calculate the value of \( \sin \theta \) using degree and radians.**
- \( \sin \theta = \underline{\hspace{80px}} \)
You should get the same value for \( \sin \theta \) if \( \theta \) is in radians.
**Refer to the lab manual G-7 to calculate the uncertainty in \( \sin \theta \).**
- \(\delta (\sin \theta)/\sin \theta =\)
- \(\delta (\sin \theta) =\)
**Additional Notes:**
The side where the ray incident on the boundary is referred to as medium 1, and the side with the refracted ray as medium 2. If the index of refraction of medium 2 is smaller than that of medium 1, total internal reflection could occur. The critical angle \( \theta_c \) is given by:
\[ \sin \theta_c = n_2/n_1 \]
If \( n_2 \) is known, the index of refraction of the incident side can be calculated using \( \theta_c \). If \( n_2 = 1.00 \) and \( \theta_c = 40^\circ \pm 1^\circ \), calculate the value of \( n_1 \) and its uncertainty.
- \( n_1 = \underline{\hspace{150px}} \)
- \( \delta n_1 = \underline{\hspace{150px}} \)
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