Question

A beam containing light of wavelengths λ1 and λ2 passes through a set of parallel slits. In the interference pattern, the fourth bright line of the λ1 light occurs at the same position as the fifth bright line of the λ2 light. If λ1 is known to be 530 nm, what is the value for λ2?

Answer 1

Answer:

Unknown wavelength of light is

$\lambda_2 = 424 nm$

Explanation:

In Young's double slit experiment we know that position of bright fringe is given as

$y\frac{d}{L} = N\lambda$

so we have

$y = \frac{N\lambda L}{d}$

here we know that position of 4th bright fringe of first wavelength is same as the position of 5th bright fringe of second wavelength

here we know that

$\lambda_1 = 530 nm$

now we have

$N_1\lambda_1\frac{L}{d} = N_2\lambda_2\frac{L}{d}$

$4 \times 530 nm = 5 \times \lambda_2$

$\lambda_2 = 424 nm$