Two slits are 0.144 mm apart. A mixture of red light (wavelength = 665 nm) and yellow-green light (wavelength = 565 nm) falls on the slits. A flat observation screen is located 2.11 m away. What is the distance on the screen between the third-order red fringe and the third-order yellow-green fringe?

To find the distance between the third-order red fringe and the third-order yellow-green fringe, we can use the formula for the fringe separation in Young's double-slit experiment:

Δy = (λ * L) / d

Where:
Δy = Fringe separation (distance between two adjacent fringes on the screen)
λ = Wavelength of light
L = Distance from the double slits to the screen
d = Distance between the double slits

Let's calculate the fringe separation for the red light:

For red light (λ = 665 nm = 665 * 10^(-9) m)
L = 2.11 m
d = 0.144 mm = 0.144 * 10^(-3) m

Δy_red = (665 * 10^(-9) * 2.11) / (0.144 * 10^(-3))

Now let's calculate the fringe separation for the yellow-green light:

For yellow-green light (λ = 565 nm = 565 * 10^(-9) m)
L = 2.11 m
d = 0.144 mm = 0.144 * 10^(-3) m

Δy_yellow-green = (565 * 10^(-9) * 2.11) / (0.144 * 10^(-3))

Finally, we can subtract Δy_yellow-green from Δy_red to find the distance between the third-order red fringe and the third-order yellow-green fringe:

Distance = Δy_red - Δy_yellow-green

Now, let's plug in the values and calculate the result.