If light illuminates a double slit an interference pattern of alternating bright and dark spots is seen. The intensity of the bright spots is brighter at the centre due to the width of the slits. The bright interference fringes will be readily observed inside the broad central diffraction maximum. Outside this they will be much fainter.A laser of wavelength λ = 650 nm is shone on a pair of slits each of width a = 31 µm. The slit spacing is d = 0.3 mm. The resulting interference pattern is projected on to a screen a distance L= 2.6 m from the double slit.Counting out from the (n= 0) central bright interference fringe, how many more bright interference fringes will be seen before the intensity drops to zero at the edge of the central diffraction maximum.Express your answer to the nearest whole number.
Question
If light illuminates a double slit an interference pattern of alternating bright and dark spots is seen. The intensity of the bright spots is brighter at the centre due to the width of the slits. The bright interference fringes will be readily observed inside the broad central diffraction maximum. Outside this they will be much fainter.A laser of wavelength λ = 650 nm is shone on a pair of slits each of width a = 31 µm. The slit spacing is d = 0.3 mm. The resulting interference pattern is projected on to a screen a distance L= 2.6 m from the double slit.Counting out from the (n= 0) central bright interference fringe, how many more bright interference fringes will be seen before the intensity drops to zero at the edge of the central diffraction maximum.Express your answer to the nearest whole number.
Solution
To solve this problem, we need to use the formula for the angular position of the minima in the diffraction pattern of a single slit, which is given by:
θ = m * λ / a
where:
- m is the order of the minima,
- λ is the wavelength of the light, and
- a is the width of the slit.
We are looking for the first minimum (m=1), so we can substitute these values into the formula:
θ = 1 * 650e-9 m / 31e-6 m = 0.021
This is the angle in radians at which the intensity of the diffraction pattern drops to zero.
Next, we need to find the angular position of the bright fringes in the interference pattern of a double slit, which is given by:
θ' = n * λ / d
where:
- n is the order of the fringe, and
- d is the spacing between the slits.
We can rearrange this formula to solve for n:
n = θ' * d / λ
Substituting the values we have:
n = 0.021 * 0.3e-3 m / 650e-9 m = 9.7
Since we can't have a fraction of a fringe, we round this to the nearest whole number, which gives us 10.
So, counting out from the central bright interference fringe (n=0), 10 more bright interference fringes will be seen before the intensity drops to zero at the edge of the central diffraction maximum.
Similar Questions
f light illuminates a double slit an interference pattern of alternating bright and dark spots is seen. The intensity of the bright spots is brighter at the centre due to the width of the slits. The bright interference fringes will be readily observed inside the broad central diffraction maximum. Outside this they will be much fainter.A laser of wavelength λ = 650 nm is shone on a pair of slits each of width a = 17 µm. The slit spacing is d = 0.2 mm. The resulting interference pattern is projected on to a screen a distance L= 2.6 m from the double slit.Counting out from the (n= 0) central bright interference fringe, how many more bright interference fringes will be seen before the intensity drops to zero at the edge of the central diffraction maximum.Express your answer to the nearest whole number.
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 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= 2.35 m from the slits. From one dark spot 7 further dark spots are counted and the distance is measured to be Z = 0.093 m.Calculate the wavelength λ of the laser.
Light from He-Ne laser (𝜆 = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen located 3.0 m behind the slits. Eleven bright fringes are seen, spanning 5.2 cm. a. Can a small angle approximation be used? b. What is the separation between the slits?
Explain how the interference of light waves creates bright and dark patches in the double-slit experiment.Refer to the model in the previous question to support your answer.
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.