A monochromatic light of wavelength 587.5nm illuminates a slit of width 0.75mm. At what distance from the slit should a screen be placed so that the first dark fringe is at 0.85mm from the center of the diffraction pattern?
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html
solve for d.
To find the distance from the slit to the screen where the first dark fringe occurs, we can use the formula for the angular position of the dark fringe in a single-slit diffraction pattern:
θ = λ / (2 * b)
Where:
θ is the angular position of the dark fringe
λ is the wavelength of the light
b is the width of the slit
First, convert the wavelength from nanometers to meters:
λ = 587.5 nm = 587.5 x 10^-9 m
Next, convert the slit width from millimeters to meters:
b = 0.75 mm = 0.75 x 10^-3 m
Now, substitute the values into the equation:
θ = (587.5 x 10^-9 m) / (2 * (0.75 x 10^-3 m))
Calculate the value of θ.
Next, we can use trigonometry to find the distance from the slit to the screen, assuming small angles:
tan(θ) = opposite / adjacent
The opposite side represents the distance from the center of the diffraction pattern to the location of the dark fringe, which is 0.85 mm. Convert this to meters:
opposite = 0.85 mm = 0.85 x 10^-3 m
In this case, the distance from the slit to the screen is the adjacent side.
Rearrange the equation to solve for the adjacent side:
adjacent = opposite / tan(θ)
Substitute the values of opposite and θ into the equation, and calculate the value of adjacent. This will give you the distance from the slit to the screen where the first dark fringe occurs.