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?

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)

To find the unknown wavelength in the double-slit experiment, we can use the equation:

λ = (m * d * L) / y

where:
λ is the wavelength
m is the order of the maximum
d is the distance between the slits
L is the distance from the slits to the screen
y is the distance between the central bright spot and the mth-order maximum

Let's use this equation to calculate the unknown wavelength.

For the known wavelength (480 nm) case:
m = 3 (third-order maximum)
d = ?
L = 1.8 m
y = 12 mm = 0.012 m

Rearranging the equation:
d = (λ * y) / (m * L)
d = (480 nm * 0.012 m) / (3 * 1.8 m)
d = 0.0048 m

Now, we can use the calculated slits distance to find the unknown wavelength for the second-order maximum case.

m = 2 (second-order maximum)
d = 0.0048 m
L = 1.8 m
y = 14.9 mm = 0.0149 m

Rearranging the equation:
λ = (m * d * L) / y
λ = (2 * 0.0048 m * 1.8 m) / 0.0149 m
λ = 0.046889 m

To convert this to nanometers (nm), we multiply by 10^9:
λ = 0.046889 m * 10^9 nm/m
λ ≈ 46.889 nm

Therefore, the unknown wavelength is approximately 46.889 nm.