What is the process to calculate the distance between the fringes on a viewing screen when a light of wavelength 460 nm falls on two slits immersed in water?
To calculate the distance between the fringes on a viewing screen when a light of wavelength 460 nm falls on two slits immersed in water, we first need to convert the distance between the slits to meters. Then, we calculate the wavelength of light in water using the refractive index of water. Finally, we use the formula for fringe separation to determine the distance between the fringes on the screen.
Calculating Fringe Separation of Light Wavelength in Water
1. Convert Distance Between Slits to Meters:
The distance between the slits is given as 6.30×10^(-2) mm.
Convert this to meters: 6.30×10^(-2) mm = 6.30×10^(-5) m.
2. Calculate Wavelength of Light in Water:
The wavelength of light in water can be calculated using the formula:
λ(water) = λ(air) / n
where λ(air) is the wavelength of light in the air (460 nm) and n is the refractive index of water (approximately 1.33).
Calculate: λ(water) = 460 × 10^(-9) m / 1.33.
3. Determine Fringe Separation:
To find the fringe separation, use the formula:
d = λ(water) * L / D
where d is the fringe separation, L is the distance between the slits and the screen (0.43 m in this case), and D is the distance between the slits and the observer.
Substitute the values and calculate: d = (460 × 10^(-9) m / 1.33) * 0.43 m / D.
Since the distance between the slits and the observer (D) is not provided, the exact distance between the fringes on the screen cannot be calculated accurately without this value.
This process involves converting units, calculating wavelength in a different medium (water), and applying the formula for fringe separation to determine the distance between the fringes on a viewing screen when light of a certain wavelength falls on two slits immersed in water.