Question

Write down the formula for the distances of nth bright and nth dark fringes, from the central fringe in Young's double slit experiment. A monochromatic source of light with wavelength 480 nm, is used in this experiment, in which distance between the double slits is 3 mm. Distance between the slits and screen is 2 m. Find the distance between the 8th bright and the 3rd dark fringes.

Hint:

In Young's double slit experiment, the distance between bright or dark fringes depends on the wavelength of light, the slit separation, and the distance to the screen. For dark fringes, the fringe position is slightly shifted by \( \frac{1}{2} \lambda \).

Answer 1

In Young's double slit experiment, the formula for the distance of the nth bright fringe (denoted as \( y_n \)) from the central maximum is given by:
\[ y_n = \frac{n \lambda L}{d} \] Where: - \( n \) is the fringe number (for bright fringes, \( n = 1, 2, 3, \ldots \)),
- \( \lambda \) is the wavelength of light (given as \( 480 \, \text{nm} \) or \( 480 \times 10^{-9} \, \text{m} \)),
- \( L \) is the distance between the slits and the screen (given as \( 2 \, \text{m} \)),
- \( d \) is the distance between the slits (given as \( 3 \, \text{mm} \) or \( 3 \times 10^{-3} \, \text{m} \)).
For the nth dark fringe, the distance from the central fringe is given by the formula:
\[ y'_n = \frac{(n - 1/2) \lambda L}{d} \] To find the distance between the 8th bright and the 3rd dark fringes, we calculate the distance for the 8th bright fringe (\( y_8 \)) and the 3rd dark fringe (\( y'_3 \)). 1. Distance for the 8th bright fringe: \[ y_8 = \frac{8 \times 480 \times 10^{-9} \times 2}{3 \times 10^{-3}} = 0.00384 \, \text{m} = 3.84 \, \text{mm} \] 2. Distance for the 3rd dark fringe: \[ y'_3 = \frac{(3 - 1/2) \times 480 \times 10^{-9} \times 2}{3 \times 10^{-3}} = 0.00480 \, \text{m} = 4.80 \, \text{mm} \] Now, to find the distance between the 8th bright and the 3rd dark fringes:
\[ \text{Distance} = y'_3 - y_8 = 4.80 \, \text{mm} - 3.84 \, \text{mm} = 0.96 \, \text{mm} \] Thus, the distance between the 8th bright and the 3rd dark fringes is \( 0.96 \, \text{mm} \).