(a) White light is spread out into its spectral components by a diffraction grating. If the grating has 1,990 grooves per centimeter, at what angle (in degrees) does red light of wavelength 640 nm appear in first order? (Assume that the light is incident normally on the gratings.) (b) What If? What is the angular separation (in degrees) between the first-order maximum for 640 nm red light and the first- order maximum for orange light of wavelength 600 nm?
(a) White light is spread out into its spectral components by a diffraction grating. If the grating has 1,990 grooves per centimeter, at what angle (in degrees) does red light of wavelength 640 nm appear in first order? (Assume that the light is incident normally on the gratings.) (b) What If? What is the angular separation (in degrees) between the first-order maximum for 640 nm red light and the first- order maximum for orange light of wavelength 600 nm?
Related questions
Question
![### Diffraction Grating Angular Separation
---
#### Problem Statement:
(a) White light is spread out into its spectral components by a diffraction grating. If the grating has **1,990 grooves per centimeter**, at what angle (in degrees) does red light of wavelength **640 nm** appear in first order? (Assume that the light is incident normally on the gratings.)
`___________°`
(b) **What If?** What is the angular separation (in degrees) between the first-order maximum for **640 nm red light** and the first-order maximum for **orange light of wavelength 600 nm**?
`___________°`
---
### Explanation:
- **Part (a)** requires the calculation of the diffraction angle for red light using the known number of grooves per centimeter and the wavelength of the light.
- **Part (b)** involves finding the angular separation between the first-order maxima for red and orange light, given their respective wavelengths and the same grating conditions.
The formulas that might be helpful in solving these problems include the diffraction grating equation:
\[ d \sin(\theta) = n \lambda \]
where:
- \( d \) is the distance between adjacent grating lines (the inverse of the number of grooves per centimeter),
- \( \theta \) is the angle of diffraction,
- \( n \) is the order of the maximum (first-order in this case, so \( n = 1 \)),
- \( \lambda \) is the wavelength of the light.
By solving these equations, one can determine the required angles.
This method highlights the practical application of diffraction gratings in separating light into its spectral components, an essential concept in optics and spectroscopy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feafc6826-5c88-4b32-b630-d072d1855c17%2F1fa9fef3-ed8c-4cf7-83a7-87d997c76ff3%2Fxsimst_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Diffraction Grating Angular Separation
---
#### Problem Statement:
(a) White light is spread out into its spectral components by a diffraction grating. If the grating has **1,990 grooves per centimeter**, at what angle (in degrees) does red light of wavelength **640 nm** appear in first order? (Assume that the light is incident normally on the gratings.)
`___________°`
(b) **What If?** What is the angular separation (in degrees) between the first-order maximum for **640 nm red light** and the first-order maximum for **orange light of wavelength 600 nm**?
`___________°`
---
### Explanation:
- **Part (a)** requires the calculation of the diffraction angle for red light using the known number of grooves per centimeter and the wavelength of the light.
- **Part (b)** involves finding the angular separation between the first-order maxima for red and orange light, given their respective wavelengths and the same grating conditions.
The formulas that might be helpful in solving these problems include the diffraction grating equation:
\[ d \sin(\theta) = n \lambda \]
where:
- \( d \) is the distance between adjacent grating lines (the inverse of the number of grooves per centimeter),
- \( \theta \) is the angle of diffraction,
- \( n \) is the order of the maximum (first-order in this case, so \( n = 1 \)),
- \( \lambda \) is the wavelength of the light.
By solving these equations, one can determine the required angles.
This method highlights the practical application of diffraction gratings in separating light into its spectral components, an essential concept in optics and spectroscopy.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
