The physics of interference and a student experiment. A student is measuring the wavelength of a narrow , monochromatic light source The double slit has a separation of 0.15 mm. A second student places markers on a screen 2 .0 m in front of the slits at the positions of successive dark bands in the patterns. The student finds that the dark bands are 0.56 cm apart. a. The student has met two important conditions for interference to occur What are they? b. Calculate the wavelength of the light source. c. Calculate the spacing of the dark bands if a source of wavelength 6000 nm were used. (A 147:nm@#148 ; is a nanometre, or 10^-9m. d. If a student wants the spaces between the dark bands in an interference pattern to be wider apart, should the spacing between the slits increase or decrease?

a. The two important conditions for interference to occur are:<br /><br />1. **Coherent Sources:** The two light sources (in this case, the two slits acting as sources due to diffraction) must be coherent. This means they maintain a constant phase relationship. In the double-slit experiment, this is achieved because both slits are illuminated by the same single source, ensuring the light waves emerging from them have a fixed phase difference.<br /><br />2. **Monochromatic Light:** The light source must be monochromatic, meaning it consists of a single wavelength (or a very narrow range of wavelengths). This ensures a stable interference pattern with well-defined bright and dark fringes. Different wavelengths would interfere differently, blurring the pattern.<br /><br />b. To calculate the wavelength, we can use the formula for the distance between dark fringes (also called minima) in a double-slit interference pattern:<br /><br />* Δy = (λL) / d<br /><br />Where:<br />* Δy is the distance between consecutive dark fringes (0.0056 m)<br />* λ is the wavelength of the light (what we want to find)<br />* L is the distance from the slits to the screen (2.0 m)<br />* d is the separation between the slits (0.00015 m)<br /><br />Rearranging the formula to solve for λ:<br /><br />* λ = (Δy * d) / L<br />* λ = (0.0056 m * 0.00015 m) / 2.0 m<br />* λ = 4.2 x 10⁻⁷ m, or 420 nm<br /><br />c. To calculate the spacing of the dark bands with a 6000 nm (6.0 x 10⁻⁷ m) light source, we use the same formula:<br /><br />* Δy = (λL) / d<br />* Δy = (6.0 x 10⁻⁷ m * 2.0 m) / 0.00015 m<br />* Δy = 0.008 m, or 8.0 mm<br /><br />d. To make the spaces between the dark bands wider, the spacing between the slits (d) should *decrease*. This is evident from the formula Δy = (λL) / d. If d decreases (and λ and L remain constant), Δy will increase. Intuitively, bringing the slits closer together causes the diffracted waves to overlap more, resulting in a wider interference pattern.<br />