Q1. In a double-slit experiment, if the distance between the slits is increased, what happens to the distance between the interference fringes? (2021)
Solution:
The distance between the fringes decreases as fringe width β = λD/d; increasing d reduces β.
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Q2. In a Newton's rings experiment, if the radius of the nth dark ring is r_n, what is the relationship between r_n and the wavelength λ? (2021)
Solution:
The radius of the dark rings in Newton's rings is given by r_n² = nλR, where R is the radius of curvature of the lens. Thus, r_n ∝ nλ.
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Q3. In a Newton's ring experiment, if the radius of the first dark ring is found to be r, what is the radius of the second dark ring? (2020)
Solution:
The radius of the dark rings in Newton's rings is proportional to the square root of the ring number. Thus, the second dark ring will have a radius of 2r.
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Q4. What is the angle of diffraction for the first minimum in a single-slit diffraction pattern if the slit width is 0.5 mm and the wavelength of light is 500 nm? (2023)
Solution:
The angle for the first minimum is given by sin θ = λ/a, where a is the slit width. Thus, sin θ = 500 nm / 0.5 mm = 0.001, leading to θ ≈ 30°.
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Q5. What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with a slit separation of 0.1 mm and a screen distance of 1 m? (2019)
Solution:
Using the formula λ = d sin θ / m, where d = 0.1 mm, θ = 30°, and m = 1, we find λ = 0.1 mm * sin(30°) = 0.1 mm * 0.5 = 0.05 mm = 0.2 mm.
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Q6. In a thin film of oil on water, which color of light is most likely to be reflected? (2022)
Solution:
Due to the phenomenon of thin film interference, the color that is most prominently reflected depends on the thickness of the film and the wavelength of light. Typically, blue light is more likely to be reflected due to shorter wavelengths.
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Q7. What is the minimum thickness of a soap bubble for which the first order of bright fringe is observed in reflected light? (2020)
Solution:
For the first order of bright fringe in reflected light, the minimum thickness of the soap bubble is λ/4 due to the phase change upon reflection.
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Q8. In a thin film of air between two glass plates, which of the following colors will be least affected by interference? (2022)
Solution:
Red light has the longest wavelength and is least affected by interference effects in thin films compared to shorter wavelengths.
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Q9. If a thin film of oil on water produces a green color due to interference, what can be inferred about the thickness of the film? (2023)
Solution:
Thin films produce colors due to interference; a green color indicates a thin film where the thickness is comparable to the wavelength of visible light.
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Q10. What is the path difference for the first minimum in a single-slit diffraction pattern? (2021)
Solution:
The path difference for the first minimum in single-slit diffraction is λ/2.
