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A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincides. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (in nm) (Nearest integer)
    Correct answer is '443'. Can you explain this answer?
    Most Upvoted Answer
    A mixture of light, consisting of wavelength 590 nm and an unknown wa...
    Given data:
    - A mixture of light consists of two wavelengths: 590 nm and an unknown wavelength.
    - The central maximum of both lights coincides.
    - The third bright fringe of known light coincides with the fourth bright fringe of the unknown light.

    Explanation:

    Step 1: Understanding Young's double-slit experiment
    - In Young's double-slit experiment, light passes through two closely spaced slits and creates an interference pattern on a screen.
    - The interference pattern consists of alternating bright and dark fringes.
    - The central maximum is the brightest fringe, located at the center of the pattern.
    - The fringes occur due to the constructive and destructive interference of light waves.

    Step 2: Analyzing the given data
    - The central maximum of both lights coincides, indicating that the two wavelengths have the same path difference at the center.
    - The path difference between the two slits for the central maximum is zero.
    - The third bright fringe of known light coincides with the fourth bright fringe of the unknown light. This means that the path difference for these fringes is the same.

    Step 3: Using the path difference formula
    - The path difference (Δx) for bright fringes is given by Δx = mλ, where m is the order of the fringe and λ is the wavelength of light.
    - As the third bright fringe of known light coincides with the fourth bright fringe of the unknown light, the path difference for both of these fringes is the same.
    - Therefore, we can write the equation as m1λ1 = m2λ2, where m1 = 3, λ1 = 590 nm, m2 = 4, and λ2 is the unknown wavelength.

    Step 4: Calculating the unknown wavelength
    - Substituting the given values in the equation: 3 * 590 = 4 * λ2.
    - Solving the equation, we find λ2 = (3 * 590) / 4 = 442.5 nm.
    - Rounding off to the nearest integer, the wavelength of the unknown light is 443 nm.

    Therefore, the wavelength of the unknown light is 443 nm.
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    A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincides. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (in nm) (Nearest integer)Correct answer is '443'. Can you explain this answer?
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    A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincides. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (in nm) (Nearest integer)Correct answer is '443'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincides. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (in nm) (Nearest integer)Correct answer is '443'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincides. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (in nm) (Nearest integer)Correct answer is '443'. Can you explain this answer?.
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