Find the distance on a flat screen between the principal image and the second order bright fringe for red light(wavelength=664nm)if there are 900 slits per centimeter and the screen is 2.75 meters from the slits.
.01 meter/900 = 1.11*10^-5 meters`
sin T = T = 664*10^-9/1.11*10^-5 = .0598
.0598 * 2.75 = .164 meters
To find the distance between the principal image and the second order bright fringe for red light in this setup, we can use the equation for the position of the bright fringes in a single-slit diffraction pattern:
y = (m * λ * L) / d
where:
- y is the distance from the principal image to the fringe (in meters)
- m is the order of the bright fringe (in this case, m = 2 for second order)
- λ is the wavelength of the light (in meters)
- L is the distance between the slits and the screen (in meters)
- d is the distance between the slits (in meters)
First, we need to convert the given values to meters:
- The wavelength of the red light is given as 664 nm, so λ = 664 nm * 10^-9 m/nm = 6.64 * 10^-7 m.
- The number of slits per centimeter is given as 900 slits/cm, so the distance between the slits d = 1 cm / 900 = 0.0011 m.
Now, we can substitute the values into the equation:
y = (2 * 6.64 * 10^-7 m * 2.75 m) / 0.0011 m
y = (1.7288 * 10^-6 m) / (0.0011 m)
y ≈ 1.57 * 10^-3 m
Therefore, the distance between the principal image and the second order bright fringe for red light is approximately 1.57 * 10^-3 meters.