A light beam strikes a piece of glass at a 46.44° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. Part A What is the angle between the two refracted beams? Express your answer using two significant figures. 0.16
A light beam strikes a piece of glass at a 46.44° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. Part A What is the angle between the two refracted beams? Express your answer using two significant figures. 0.16
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please help with this i couldnt get the right answer
![**Problem 32.53**
A light beam strikes a piece of glass at a 46.44° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively.
---
**Part A**
*What is the angle between the two refracted beams?*
*Express your answer using two significant figures.*
θ = [ ]
[Submit Button]
*Incorrect; Try Again; 3 attempts remaining*
---
### Explanation of Solution Process
1. **Incident Angle**: The angle at which the light beam strikes the glass is 46.44°.
2. **Wavelengths and Indices**:
- Wavelength 1: 450.0 nm with an index of refraction of 1.4831.
- Wavelength 2: 700.0 nm with an index of refraction of 1.4754.
3. **Calculation Requirement**: Determine the angle between the two refracted beams within the glass based on their differing indices of refraction.
4. **Method**:
- Use Snell's Law: \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \)
- Calculate the refraction angle for each wavelength using the given indices.
- Determine the difference between these angles to find the angle between the two beams.
5. **Input and Feedback**:
- The answer inputs a value of -0.16.
- Feedback indicates the response is incorrect.
- Three attempts are remaining for submission.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0585e2c7-27a9-4fc0-a2a5-2addf480d0e1%2F94d8c4e0-a2bc-4a4a-8abc-9859df7707cf%2Fp68ikgt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 32.53**
A light beam strikes a piece of glass at a 46.44° incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively.
---
**Part A**
*What is the angle between the two refracted beams?*
*Express your answer using two significant figures.*
θ = [ ]
[Submit Button]
*Incorrect; Try Again; 3 attempts remaining*
---
### Explanation of Solution Process
1. **Incident Angle**: The angle at which the light beam strikes the glass is 46.44°.
2. **Wavelengths and Indices**:
- Wavelength 1: 450.0 nm with an index of refraction of 1.4831.
- Wavelength 2: 700.0 nm with an index of refraction of 1.4754.
3. **Calculation Requirement**: Determine the angle between the two refracted beams within the glass based on their differing indices of refraction.
4. **Method**:
- Use Snell's Law: \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \)
- Calculate the refraction angle for each wavelength using the given indices.
- Determine the difference between these angles to find the angle between the two beams.
5. **Input and Feedback**:
- The answer inputs a value of -0.16.
- Feedback indicates the response is incorrect.
- Three attempts are remaining for submission.
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