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In young's double slit experiment, interference pattern is observed on the screen L distance apart from slits, average distance between adjacent fringes is x and slits separation is d, then the wavelength of light will be _
- a)xd/ L
- b)xL/d
- c)Ld/x
- d)Ldx
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In youngs double slit experiment, interference pattern is observed on ...
Fringe width = λD/d
where λ us wavelength
D is the distance between slits & screen
d is the distance between slits
ATQ: x = Lλ/d => λ = xd/L
where λ us wavelength
D is the distance between slits & screen
d is the distance between slits
ATQ: x = Lλ/d => λ = xd/L
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
In youngs double slit experiment, interference pattern is observed on ...
Young's double-slit experiment involves a setup with two closely spaced slits through which light passes. When the light waves from the two slits overlap, they interfere with each other, creating an interference pattern on a screen placed at a distance L from the slits.
- **Key information:**
- Distance between the slits: d
- Distance between the screen and the slits: L
- Average distance between adjacent fringes: x
- **Interference pattern:**
- When the light waves from the two slits reach the screen, they interfere constructively and destructively, creating a pattern of bright and dark fringes.
- The bright fringes correspond to constructive interference, where the waves from the two slits arrive in phase and reinforce each other.
- The dark fringes correspond to destructive interference, where the waves from the two slits arrive out of phase and cancel each other.
- **Deriving the formula:**
- The distance between adjacent fringes can be determined by considering the path difference between the waves from the two slits.
- The path difference, denoted as δ, is given by δ = λ * sinθ, where λ is the wavelength of light and θ is the angle between the incident light and the screen.
- In the double-slit setup, the angle θ can be approximated as θ ≈ tanθ ≈ y/L, where y is the distance from the central bright fringe to a particular fringe.
- Therefore, the path difference can be written as δ = λ * y/L.
- For constructive interference, the path difference must be an integer multiple of the wavelength: δ = m * λ, where m is an integer (m = 0, ±1, ±2, ...).
- Equating the two expressions for δ, we have λ * y/L = m * λ.
- Solving for y, we get y = m * L.
- The average distance between adjacent fringes is given by x = 2y = 2m * L.
- **Final step:**
- Comparing the derived formula for x with the given options, we find that the correct answer is option 'A': xd/L.
- **Key information:**
- Distance between the slits: d
- Distance between the screen and the slits: L
- Average distance between adjacent fringes: x
- **Interference pattern:**
- When the light waves from the two slits reach the screen, they interfere constructively and destructively, creating a pattern of bright and dark fringes.
- The bright fringes correspond to constructive interference, where the waves from the two slits arrive in phase and reinforce each other.
- The dark fringes correspond to destructive interference, where the waves from the two slits arrive out of phase and cancel each other.
- **Deriving the formula:**
- The distance between adjacent fringes can be determined by considering the path difference between the waves from the two slits.
- The path difference, denoted as δ, is given by δ = λ * sinθ, where λ is the wavelength of light and θ is the angle between the incident light and the screen.
- In the double-slit setup, the angle θ can be approximated as θ ≈ tanθ ≈ y/L, where y is the distance from the central bright fringe to a particular fringe.
- Therefore, the path difference can be written as δ = λ * y/L.
- For constructive interference, the path difference must be an integer multiple of the wavelength: δ = m * λ, where m is an integer (m = 0, ±1, ±2, ...).
- Equating the two expressions for δ, we have λ * y/L = m * λ.
- Solving for y, we get y = m * L.
- The average distance between adjacent fringes is given by x = 2y = 2m * L.
- **Final step:**
- Comparing the derived formula for x with the given options, we find that the correct answer is option 'A': xd/L.
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In youngs double slit experiment, interference pattern is observed on the screen L distance apart from slits, average distance between adjacent fringes is x and slits separation is d, then the wavelength of light will be _a)xd/ Lb)xL/dc)Ld/xd)LdxCorrect answer is option 'A'. Can you explain this answer?
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