Question

(d) In young’s double slit experiment, the distance between the slits is 1.75mm and the viewing source is placed at the distance of 1.5m from the slits. The third order dark fringe is 5.0cm from the center line. a. Determine the wavelength of the light. b. Calculate the distance between adjacent dark fringes.

Answer 1

Given:

In young’s double slit experiment, the distance between the slits is 1.75mm and the viewing source is placed at the distance of 1.5m from the slits. The third order dark fringe is 5.0cm from the center line.

To find:

• Wavelength of light

• Fringe width

Calculation:

The 3rd order dark fringe is located 5 cm from centre line ;

$\therefore \: \dfrac{(2n + 1) \lambda D}{2d} = x$

Putting all distance units in mm :

$= > \: \dfrac{ \{(2 \times 3) + 1 \} \lambda \times (1500)}{2 \times 1.75} = 50$

$= > \: \dfrac{ \{7\} \lambda \times (1500)}{3.5} = 50$

$= > \: \{7\} \lambda \times (428.57) = 50$

$= > \: \{7\} \lambda \times 8.57= 1$

$= > 60 \lambda = 1$

$= > \lambda = 0.0166 \: mm$

$= > \lambda = 16.6 \: \mu m$

So wavelength of light is 14.2 micro-metre.

Fringe width is denoted by $\beta$

$\beta = \dfrac{ \lambda D}{d}$

$= > \beta = \dfrac{ 0.0166 \times 1500}{1.75}$

$= > \beta = 14.22 \: mm$

So fringe width is 14.22 mm.