Calculating Wavelength of Incident Light

What is the wavelength of the incident light?

Given that light from a monochromatic source shines through a double slit onto a screen 5.00 m away, with the slits being 0.180 mm apart and the dark bands on the screen measured to be 1.70 cm apart, what is the wavelength of the incident light?

Answer:

The wavelength of the incident light which shines from a monochromatic source is 612 nm.

Wavelength is nothing but the distance between two consecutive waves. In this scenario, we have the distance between the screen and the slit as 5 m, the slit width as 0.180 mm, and the width of the fringe as 1.7 cm.

The relation between the width of the fringe (β), slit width (d), the distance to the screen (x), and the wavelength (λ) can be expressed as β = (x * λ) / d. Solving for the wavelength, we get λ = (β * d) / x.

Substituting the given values, we have λ = (0.017 * 0.180 * 10^-3) / 5 = 6.12 * 10^-7 = 617 nm. Therefore, the wavelength of the incident light is 612 nm.

This calculation is crucial in understanding the properties of light and how it behaves in different scenarios. By determining the wavelength of the incident light, we can further explore the nature of light and its interaction with various mediums.