Final answer:
The separation between the double slits is approximately 0.159 mm when light of 575 nm wavelength passes through and the third order bright fringe is observed at an angle of 6.5 degrees.
Step-by-step explanation:
The separation between the double slits when light of wavelength 575 nm passes through and the third order bright fringe is observed at an angle of 6.5 degrees can be calculated using the formula for double-slit interference,
which is d sin(θ) = mλ, where d is the distance between the slits, θ is the angle from the central maximum to the m-th order maximum, m is the order of the maximum, and λ is the wavelength of light. In this case, m is 3 and λ is 575 nm (which is 575 x 10^-9 meters).
To find d, rearrange the formula to d = mλ / sin(θ).
Plugging in the provided numbers: d = (3 x 575 x 10^-9 m) / sin(6.5 degrees).
Using a calculator, we find that d to be approximately 0.159 mm.