Question 4 of 8intermediate🔧 ApplyNumerical3 marks

In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Correct Answer

The wavelength of light used in the experiment is 600 nm.

Exercise: EXERCISES | Q: 10.4 | (Chapter: Page 19)
For More Understanding

Explanation

To find the wavelength, we use the standard formula for the position of bright fringes in Young's double-slit experiment, which relates fringe width, slit separation, and screen distance. The distance between the central bright fringe and the fourth bright fringe corresponds to four fringe widths.

Solution Steps

  1. Step 1: Identify the given values from the question. The slit separation is d = 0.28 mm = 0.28×100.28 \times 10⁻³ m, the distance to the screen is D = 1.4 m, and the distance between the central bright fringe and the fourth bright fringe is y = 1.2 cm = 1.2×101.2 \times 10⁻² m. The fringe number is n = 4.

  2. Step 2: State the relationship for the position of the nth bright fringe. The distance y is given by the formula y = (n λ D) / d.

  3. Step 3: Rearrange the formula to solve for the wavelength λ: λ = (y d) / (n D).

  4. Step 4: Substitute the values into the formula: λ = (1.2×101.2 \times 10⁻² m × 0.28×100.28 \times 10⁻³ m) / (4×1.44 \times 1.4 m).

  5. Step 5: Calculate the result. λ = (0.336×100.336 \times 10⁻⁵) / 5.6 = 0.06×100.06 \times 10⁻⁵ m = 6×106 \times 10⁻⁷ m.

  6. Step 6: Convert to nanometers. λ = 600×10600 \times 10⁻⁹ m = 600 nm.

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