wavelength

Question

An unknown wavelength of light is incident on a diffraction grating with 2600 lines/cm. The distance between the central antinode and the 3^rd dark node is 28.0cm when the screen is located 53.0 cm from the grating. The wavelength of the light is ___x10^-7m

Answer 1

Diffraction Grating = 2600 lines/cm

The Distance between two slits d = (1 cm / Diffraction Grating) = (1 * 10^-2)/(2600) = 3.846 * 10^-6 m

Distance between screen and slit L is 53.0 cm = 53 * 10^-2 m

Third Dark node means m = 2.5

Distance between third Dark node and Central antinode y = 28 cm = 28 * 10^-2 m

Young's Equation is λ = ( y * d) / (m * L)

λ = (28 * 10^-2  * 3.846 * 10^-6 ) / (2.5 * 53 * 10^-2 )

λ = 8.127 * 10^-7 m

λ = 812.7 * 10^-9 m

λ = 812.7 nm

Therefore the wavelength of light is 812.7 nm.