In a single-slit diffraction pattern, the distance between the first and second minima is 4.2cm on a screen 3.8m from the slit. Find the slit width given that the wavelength of the light is 530nm.
Answer in mm
Somebody please help!
To find the slit width, we can use the formula for the position of the minima in a single-slit diffraction pattern:
d * sinθ = m * λ
Where:
- d is the slit width
- θ is the angle between the central maximum and the desired minimum
- m is the order of the minimum (in this case, 1 for the first minimum)
- λ is the wavelength of the light
First, let's find the angle by considering the distance between the screen and the slit:
θ = (distance between the slit and the first minimum) / (distance between the screen and the slit)
θ = 4.2 cm / 3.8 m
θ = 0.042 m / 3.8 m
θ ≈ 0.011
Now, we can substitute the values into the formula to find the slit width:
d * sin(0.011) = 1 * 530 nm
To convert the wavelength from nanometers to meters, divide it by 10^9:
d * sin(0.011) = 1 * (530 nm / 10^9)
Simplifying the equation:
d * sin(0.011) = 5.3 x 10^-7 m
d ≈ (5.3 x 10^-7 m) / sin(0.011)
Finally, multiply the result by 1000 to convert the slit width from meters to millimeters:
d ≈ (5.3 x 10^-7 m) / sin(0.011) * 1000
Calculating this value will give you the slit width in millimeters.