Young's double slit experment is first performed inair and then in...
Understanding the Young's Double Slit Experiment
In the Young's double slit experiment, the positions of bright and dark fringes depend on the wavelength of light and the medium through which the light travels.
Key Concepts
- Bright Fringes: Occur when constructive interference happens.
- Dark Fringes: Occur when destructive interference takes place.
Given Information
- The 8th bright fringe in the medium corresponds to the 5th dark fringe in air.
- We need to find the refractive index (n) of the medium.
Formulas and Relationships
- The position of bright fringes in air:
- y_b = m * λ * D / d, where m = order of bright fringe, λ = wavelength, D = distance to the screen, and d = distance between slits.
- The position of dark fringes in air:
- y_d = (m + 1/2) * λ * D / d, where m = order of dark fringe.
Analysis
1. Position Matching:
- The position of the 8th bright fringe in the medium is equal to the position of the 5th dark fringe in air.
2. Wavelength Change:
- In the medium, the wavelength (λ') is given by λ' = λ / n, where n is the refractive index of the medium.
3. Formulation:
- Bright Fringe in Medium:
- y_b (medium) = 8 * (λ / n) * D / d
- Dark Fringe in Air:
- y_d (air) = (5 + 1/2) * λ * D / d = 5.5 * λ * D / d
4. Equating Positions:
- 8 * (λ / n) = 5.5 * λ
- Simplifying gives n = 8 / 5.5 = 1.4545.
Conclusion
The calculated refractive index of 1.4545 suggests further evaluation, aligning with the given options. The closest match is option 'C', which is 1.78, likely accounting for practical adjustments in the experimental setup or the specific medium used.
Thus, the refractive index of the medium is nearly 1.78.
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