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The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. The thickness of the air column is
(Refractive index of air μ a = 1.0003 ; Wavelength of yellow light in vacuum 6000 Å )
  • a)
    1.8 mm
  • b)
    2 mm
  • c)
    2 cm
  • d)
    2.2 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The difference in the number of wavelengths, when yellow light propaga...
Let λa and λ be the wavelengths of yellow light in air and vacuum respectively and va and c be their respective speeds in air and vacuum.
Since the frequency of light is the same in both media, we have

Now, if t is the thickness of each columm, then the number of wavelengths in the two media are
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Most Upvoted Answer
The difference in the number of wavelengths, when yellow light propaga...
Given:
- Refractive index of air (μa) = 1.0003
- Wavelength of yellow light in vacuum = 6000

Formula:
The change in number of wavelengths (\( \Delta n \)) when light passes through a medium is given by:
\[ \Delta n = \dfrac{t(\mu - 1)}{\lambda} \]
Where:
- \( \Delta n \) = Change in number of wavelengths
- \( t \) = Thickness of the medium
- \( \mu \) = Refractive index of the medium
- \( \lambda \) = Wavelength of light in vacuum

Calculation:
Given that the difference in number of wavelengths is 1, and the thickness of the air and vacuum columns is the same. Let the thickness of the air column be \( t \).
For air column:
\[ \Delta n_{air} = \dfrac{t(\mu_{a} - 1)}{\lambda} = 1 \]
\[ t(1.0003 - 1) = 6000 \]
\[ 0.0003t = 6000 \]
\[ t = \dfrac{6000}{0.0003} = 20000000 \, \text{nm} = 2 \, \text{mm} \]
Therefore, the thickness of the air column is 2 mm, which is represented by option 'b'.
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The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. The thickness of the air column is(Refractive index of air μ a = 1.0003 ; Wavelength of yellow light in vacuum 6000 )a)1.8 mmb)2 mmc)2 cmd)2.2 cmCorrect answer is option 'B'. Can you explain this answer?
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