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In the ideal double slit experiment, when a glass plate of refractive index 1.5 and thickness t is introduced in the path of one of the interfering beams of wavelength λ, the intensity at the position of central max. remains unchanged. Minimum thickness of glass plate is
- a)2λ
- b)2λ/3
- c)λ/3
- d)λ
Correct answer is option 'A'. Can you explain this answer?
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In the ideal double slit experiment, when a glass plate of refractive ...
Λ, several changes occur.
Firstly, the path length of the beam passing through the glass plate will increase due to the additional distance traveled in the glass. The increase in path length can be calculated using the formula:
ΔL = t * (n - 1)
where ΔL is the increase in path length, t is the thickness of the glass plate, and n is the refractive index of the glass.
Secondly, the wavelength of the beam passing through the glass will change according to the formula:
λ' = λ / n
where λ' is the new wavelength of the beam after passing through the glass.
These changes will affect the interference pattern observed on the screen. The interference pattern is formed due to the superposition of the two beams, and any change in their path lengths or wavelengths will alter the pattern.
The increase in path length caused by the glass plate will shift the interference fringes. The shift can be calculated using the formula:
Δx = λ * ΔL / d
where Δx is the shift in the position of the fringes, λ is the wavelength of the beam, ΔL is the increase in path length, and d is the distance between the double slits.
The change in wavelength will also affect the interference pattern. The fringes will become closer together or farther apart depending on whether the new wavelength is smaller or larger than the original wavelength.
In summary, the introduction of a glass plate in the path of one of the interfering beams will result in a shift in the interference fringes and a change in the spacing of the fringes. These changes are due to the increase in path length and the change in wavelength caused by the glass plate.
Firstly, the path length of the beam passing through the glass plate will increase due to the additional distance traveled in the glass. The increase in path length can be calculated using the formula:
ΔL = t * (n - 1)
where ΔL is the increase in path length, t is the thickness of the glass plate, and n is the refractive index of the glass.
Secondly, the wavelength of the beam passing through the glass will change according to the formula:
λ' = λ / n
where λ' is the new wavelength of the beam after passing through the glass.
These changes will affect the interference pattern observed on the screen. The interference pattern is formed due to the superposition of the two beams, and any change in their path lengths or wavelengths will alter the pattern.
The increase in path length caused by the glass plate will shift the interference fringes. The shift can be calculated using the formula:
Δx = λ * ΔL / d
where Δx is the shift in the position of the fringes, λ is the wavelength of the beam, ΔL is the increase in path length, and d is the distance between the double slits.
The change in wavelength will also affect the interference pattern. The fringes will become closer together or farther apart depending on whether the new wavelength is smaller or larger than the original wavelength.
In summary, the introduction of a glass plate in the path of one of the interfering beams will result in a shift in the interference fringes and a change in the spacing of the fringes. These changes are due to the increase in path length and the change in wavelength caused by the glass plate.
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In the ideal double slit experiment, when a glass plate of refractive index 1.5 and thickness t is introduced in the path of one of the interfering beams of wavelength λ, the intensity at the position of central max. remains unchanged. Minimum thickness of glass plate isa)2λb)2λ/3c)λ/3d)λCorrect answer is option 'A'. Can you explain this answer?
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