# Youngâ€™s Double Slit Experiment (YDSE)

Monochromatic light (single wavelength) falls on two narrow slits

*S*_{1}and*S*_{2}which are very close together acts as two coherent sources, when waves coming from two coherent sources (*S*_{1},*S*_{2}) superimpose on each other, an interference pattern is obtained on the screen. In YDSE, alternate bright and dark bands obtained on the screen. These bands are called fringes.**Fig. 9**

- Central fringe is always bright because at central position,
*Ï†*= 0Â° or Î” = 0 - The fringe pattern obtained due to a slit is more bright than that due to a point.
- If the slit widths are unequal, the minima will not be complete dark. For very large width, uniform illumination occurs.
- If one slit is illuminated with red light and the other slit is illuminated with blue light, no interference pattern is observed on the screen.
- If the two coherent sources consist of object and itâ€™s reflected image, the central fringe is dark instead of bright one.

**Fig. 10**

# Useful results

**Path difference**Path difference between the interfering waves meeting at a point

*P*on the screen is given by

Î” = Î”

*+ Î”*_{i}_{f}where Î”

*= initial path difference between the waves before the slits and Î”*_{i}*= path difference between the waves after emerging from the slits. In this case, Î”*_{f}*= 0 (commonly used condition). So*_{i}where

*x*is the position of point*P*from central maxima.For maxima at

*P*: Î” =*nÎ»*; where*n*= 0, 1, 2, â€¦ and For minima at*P*: , where*n*= 1, 2, â€¦**Location of fringe**Position of

*n*th bright fringe from central maxima, ;

*n*= 0, 1, 2 â€¦

Position of

*n*th dark fringe from central maxima**;**

*n*= 1, 2, 3 â€¦

**Fringe width (**The separation between any two consecutive bright or dark fringes is called fringe width. In

*Î²*)*YDSE*, all fringes are of equal width (Fig. 11). Fringe width,

*Î²*=

*Î»D*/

*d*, and angular fringe width

*Î¸*=

*Î»*/

*d*=

*Î²*/

*D.*

**Fig. 11**

In YDSE, if

*n*_{1}fringes are visible in a field of view with light of wavelength*Î»*_{1}, while*n*_{1}with light of wavelength*Î»*_{2}in the same field, then*n*_{1}*Î»*_{1}=*n*_{2}*Î»*_{2}.**Separation (Î”**

*x*) between fringes- Between
*n*th bright and*m*th bright fringes (*n*>*m*), Î”*x*= (*n*â€“*m*)*Î²* - Between
*n*th bright and*m*th dark fringe*n*>*m*, then*n*<*m*then