Question

In a double slit experiment, it is observed that the angular width of one fringe formed on the screen is \( 0.2^\circ \). The wavelength of light used in the experiment is 500 nm. Calculate the separation of the two slits.

Hint:

Angular fringe width = lambda/d. Convert 0.2 degree to radian and divide.

Answer 1

Step 1: Write the formula for angular fringe width:
In Young's double slit experiment, the fringe width on the screen is \( \beta = \dfrac{\lambda D}{d} \), where \( D \) is the distance of the screen and \( d \) is the slit separation.
The angular width of a fringe is \( \theta = \dfrac{\beta}{D} = \dfrac{\lambda}{d} \).

Step 2: Convert the data:
\( \theta = 0.2^\circ = 0.2 \times \dfrac{\pi}{180} = 3.49 \times 10^{-3} \) rad.
\( \lambda = 500\ \text{nm} = 5 \times 10^{-7} \) m.

Step 3: Find d:
\( d = \dfrac{\lambda}{\theta} = \dfrac{5 \times 10^{-7}}{3.49 \times 10^{-3}} = 1.43 \times 10^{-4} \) m.
This is about 0.14 mm.

Final Answer:
The slit separation is \( d \approx 1.43 \times 10^{-4} \) m (about 0.14 mm).