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In a double slit experiment two parallel slits are illuminated first by light of wacelength 400 nm and then by light of unknown wavelength. The fourth order dark fringe resuliting from the known wavelength of light falls in the same place on the screen as the second order bright fringe from the unknown wave length. The value of unknown wavelength of the light is 
  • a)
    900 nm
  • b)
    400 nm
  • c)
    300 nm
  • d)
    600 nm
Correct answer is option 'A'. Can you explain this answer?
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Given:
- Wavelength of light used in the double-slit experiment: 400 nm
- Fourth order dark fringe from the known wavelength coincides with the second order bright fringe from the unknown wavelength

To Find:
The unknown wavelength of light used in the experiment

Explanation:
The double-slit experiment is a classic experiment that demonstrates the wave-like nature of light. In this experiment, light passes through two parallel slits and creates an interference pattern on a screen placed behind the slits. The pattern consists of alternating bright and dark fringes.

Interference Pattern:
When two waves interfere constructively, they produce a bright fringe, and when they interfere destructively, they produce a dark fringe. The position of the fringes depends on the path difference between the waves.

Path Difference:
For the double-slit experiment, the path difference (δ) can be calculated using the formula:
δ = d * sin(θ)

where:
- δ is the path difference
- d is the distance between the slits
- θ is the angle between the line connecting the slits and the line from the slits to the point on the screen

Fourth Order Dark Fringe:
For the known wavelength of light (400 nm), the fourth order dark fringe occurs when the path difference is equal to 4 times the wavelength:
δ_known = 4 * λ_known

Second Order Bright Fringe:
For the unknown wavelength of light, the second order bright fringe occurs when the path difference is equal to 2 times the wavelength:
δ_unknown = 2 * λ_unknown

Equating the Path Differences:
Since the fourth order dark fringe from the known wavelength coincides with the second order bright fringe from the unknown wavelength, we can equate the path differences:
δ_known = δ_unknown

4 * λ_known = 2 * λ_unknown

Calculating the Unknown Wavelength:
Substituting the known wavelength (400 nm) into the equation:
4 * 400 nm = 2 * λ_unknown

1600 nm = 2 * λ_unknown

λ_unknown = 1600 nm / 2 = 800 nm

Therefore, the unknown wavelength of light used in the experiment is 800 nm. However, none of the given options match this result. Therefore, there may be an error in the question or options provided.
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In a double slit experiment two parallel slits are illuminated first by light of wacelength 400 nm and then by light of unknown wavelength. The fourth order dark fringe resuliting from the known wavelength of light falls in the same place on the screen as the second order bright fringe from the unknown wave length. The value of unknown wavelength of the light isa)900 nmb)400 nmc)300 nmd)600 nmCorrect answer is option 'A'. Can you explain this answer?
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