Question

In a Young’s double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the 4thx dark fringe.

Hint:

In a Young's double slit experiment, the distance between dark fringes is determined by the wavelength, the distance between the slits, and the screen distance. Use the formula \( y = \frac{n \lambda D}{d} \) to calculate the fringe positions.

Answer 1

Young's Double-Slit Experiment Given
Slit separation, \( d = 0.30 \, \text{mm} = 0.30 \times 10^{-3} \, \text{m} \)
Distance to the screen, \( D = 1.5 \, \text{m} \)
Wavelength of light, \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
We are interested in the 4th dark fringe. Position of Dark Fringes
The position of the \( n \)-th dark fringe is given by: \[ y_n = \left( n - \frac{1}{2} \right) \frac{\lambda D}{d} \] For the 4th Dark Fringe (\( n = 4 \))
\[ y_4 = \left( 4 - \frac{1}{2} \right) \frac{\lambda D}{d} = \left( 3.5 \right) \frac{\lambda D}{d} \] Substitute the Given Values
\[ y_4 = 3.5 \times \frac{600 \times 10^{-9} \times 1.5}{0.30 \times 10^{-3}} \] Calculate the Distance
\[ y_4 = 3.5 \times \frac{900 \times 10^{-9}}{0.30 \times 10^{-3}} = 3.5 \times 3 \times 10^{-3} = 10.5 \times 10^{-3} \, \text{m} \] \[ y_4 = 10.5 \, \text{mm} \] Final Answer
The distance between the central bright fringe and the 4th dark fringe is: \[ \boxed{10.5 \, \text{mm}} \]