Light of wavelength 469 nm passes through a slit, creating a diffraction pattern on a screen. The angular separation between the first diffraction minima on either side of the central maximum is 6.0∘
. Determine the width of the slit.
I used this equation to solve for the question
aSin(theta)=(m)(lamda). Which give me 4.49mircrons, but that's not the answer
the theta should be 3.0 not 6.0 degree since it said on either side
Θ may be 3º ... the wording is ???
To determine the width of the slit, we can use the formula for single-slit diffraction:
a * sin(θ) = m * λ
Where:
- a is the width of the slit
- θ is the angular separation between the first diffraction minima on either side of the central maximum
- m is the order of the diffraction minimum (here, we assume the first minimum, so m = 1)
- λ is the wavelength of light
Given:
- λ = 469 nm = 469 * 10^(-9) m
- θ = 6.0° = 6.0 * π/180 radians
Let's substitute the values into the formula:
a * sin(6.0 * π/180) = (1) * (469 * 10^(-9))
Solving for a:
a = (1 * 469 * 10^(-9)) / sin(6.0 * π/180)
Calculating the result:
a = 127.99 * 10^(-6) meters
Therefore, the width of the slit is approximately 128 μm.
To determine the width of the slit, we can use the equation you mentioned: a*sin(theta) = m*lambda. In this equation, "a" represents the slit width, "theta" is the angular separation between the first diffraction minima on either side of the central maximum (given as 6.0°), "m" is the order of the minima (which is typically an integer), and "lambda" is the wavelength of light (given as 469 nm).
In order to solve for "a", we need to rearrange the equation:
a = (m*lambda) / sin(theta)
Let's calculate it using the provided values. Since we are looking at the first diffraction minima on either side of the central maximum, we can assume m = 1.
a = (1 * 469 nm) / sin(6.0°)
Now, we need to convert the angle from degrees to radians:
angle in radians = (6.0° * pi) / 180°
Using the value of pi as 3.14159, the conversion becomes:
angle in radians = (6.0 * 3.14159) / 180
Plugging this value into the equation:
a = (1 * 469 nm) / sin((6.0 * 3.14159) / 180)
Before evaluating the equation, we need to convert the wavelength of light from nanometers to meters:
lambda = 469 nm = 469 * 10^-9 meters
Now, calculate the result:
a = (1 * 469 * 10^-9 meters) / sin((6.0 * 3.14159) / 180)
After calculating this, you should find the width of the slit. Make sure to perform the calculations correctly, and pay attention to units.