n a double-slit experiment, two different wavelengths of monochromatic light are used, one wavelength is known and the other is unknown. When the known wavelength (480 nm) is projected through the slits the third-order maximum is located 12 mm from the central bright spot on a screen 1.8 m from the slits. When the unknown wavelength is projected through the slits the second-ordert he second-order maximum is located 14.9 mm from the central bright spot on the screen. What's the unknown wavelength in nm?

Answer 1

The coordinate (location) of the 3rd maximum relative to the center of the screen is
x(k) = kLλ/d,
therefore,
x(3) = 3•L•λ1/d,
x(2) = 2•L•λ2/d,
x(3)/ x(2) =3• λ1/2• λ2,
λ2 = 3• λ1• x(2)/2• x(3) =3•480• 14.9/ 2• 12 =894 nm.
Check your given data because this wavelength is out of the visual light range (λ = 400 – 760 nm)