Question

A beam of light consisting of a known wavelength 520 nm 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.

Answer 1

Condition for Fringe Coincidence

The condition for fringe coincidence is:

\[ m_1 \lambda_1 = m_2 \lambda_2 \]

where \(m_1 = 5\), \(m_2 = 4\), and \(\lambda_1 = 520 \, \text{nm}\). Substituting:

\[ 5 \cdot 520 = 4 \cdot \lambda \Rightarrow \lambda = \frac{5 \cdot 520}{4} = 650 \, \text{nm} \]

The value of \(\lambda\) is 650 nm.