In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = (0.100 ± 0.003) mm and the pattern is projected on to the wall a distance L= (2.352 ± 0.006) m from the slits. From a dark spot 8 further dark spots are counted and the distance is measured to be Z = (12.2 ± 0.9) cm.The wavelength of the laser is calculated to be λ = 648 nm.Calculate the uncertainty in the wavelength. Express answer in nm (1x10-9m) to the nearest whole number.
Question
In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = (0.100 ± 0.003) mm and the pattern is projected on to the wall a distance L= (2.352 ± 0.006) m from the slits. From a dark spot 8 further dark spots are counted and the distance is measured to be Z = (12.2 ± 0.9) cm.The wavelength of the laser is calculated to be λ = 648 nm.Calculate the uncertainty in the wavelength. Express answer in nm (1x10-9m) to the nearest whole number.
Solution
To calculate the uncertainty in the wavelength, we first need to understand the formula that relates the slit spacing (d), the distance to the wall (L), the distance between dark spots (Z), and the wavelength (λ). This formula is given by:
λ = d * Z / (L * m)
where m is the order of the dark spot, in this case 8.
The uncertainty in a calculated quantity can be found by taking the square root of the sum of the squares of the relative uncertainties of the measured quantities. The relative uncertainty of a measured quantity is the absolute uncertainty divided by the measurement itself.
So, the relative uncertainties are:
- For d: 0.003 / 0.100 = 0.03
- For L: 0.006 / 2.352 = 0.0025
- For Z: 0.9 / 12.2 = 0.0738
- For m: since it's a counted quantity, its uncertainty is zero.
The total relative uncertainty is then:
sqrt((0.03)^2 + (0.0025)^2 + (0.0738)^2) = 0.078
To find the absolute uncertainty in the wavelength, we multiply this by the calculated wavelength:
0.078 * 648 nm = 50.544 nm
Rounding to the nearest whole number, the uncertainty in the wavelength is 51 nm.
Similar Questions
In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = 0.0001 m and the pattern is projected on to the wall a distance L= 2.23 m from the slits. From one dark spot 7 further dark spots are counted and the distance is measured to be Z = 0.097 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.
Ashton and Macie are collecting measurements for their Young's Experiment lab. The separation distance between the slits is 0.0521 mm and the interference pattern is projected onto a screen located 6.71 meters from the slits. They measure a distance from the first bright band to the central bright band to be 71.7 mm. What is the wavelength (in nanometers) of the light?
One of Mr. Chowder's lab groups is staying after school to complete the Young's Experiment investigation. They observe that light through passing two slits travels 3.93 m to a screen to produce a pattern of bright and dark bands. The group measures the distance between the first and the second bright bands on the same side of the pattern to be 18.8 mm. The slits are spaced 0.132 mm apart. What is the wavelength (in nanometers) of the light source?Wavelengthnm
A laser with a wavelength of 551 nm illuminates two narrow slits. The interference pattern from the double slits is viewed on a screen that is 1.50 m away. Over a distance of 46.0 mm there are 13.0 bright fringes with the first and last fringe situated exactly at each end of that distance. What is the spacing between the two slits?
In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.100 mm. The first-order bright fringe is measured to be 3.40 cm from the centerline. What is the wavelength of the light?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.