Question

A beam of light consisting of a known wavelength 520nm and an unknown wavelength λ, used in Young’s double slit experiment, produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of λ

Hint:

In interference problems, use the relationship between fringe order and wavelength to solve for unknowns. Coincidence of fringes gives a proportional relationship.

Answer 1

We are given that the fourth bright fringe of the unknown wavelength coincides with the fifth bright fringe of the known wavelength: \[ 4 \lambda = 5 \times 520 \, \text{nm} \] Solving for \( \lambda \): \[ \lambda = \frac{5 \times 520 \, \text{nm}}{4} = 650 \, \text{nm} \] Thus, the wavelength of the unknown light is \( 650 \, \text{nm} \).