Final answer:
The slit separation is approximately 4.61 μm for a conventional two-slit apparatus with light of wavelength 547 nm, 33 bright fringes per centimeter are observed on a screen 3 m away.
Step-by-step explanation:
Given that there are 33 bright fringes per centimeter on the screen located 3 m away and the wavelength of the light is 547 nm, we can use the formula for fringe separation to find the slit separation.
The formula for fringe separation is:
d = λL / y
where d is the fringe separation, λ is the wavelength of the light, L is the distance from the slit to the screen, and y is the number of fringes per unit distance.
Plugging in the values, we have:
d = (547 nm) * (3 m) / (33 fringes/cm * 10^4 cm/m)
Simplifying the units, we get:
d ≈ 4.61 μm
Therefore, the slit separation is approximately 4.61 μm.