Question

Two narrow slits separated by 1.5mm are illuminated by 594-nm light.

Find the distance between adjacent bright fringes on a screen 4.0m from the slits.

Express your answer to two significant figures and include the appropriate units.

Answer 1

The condition for the constructive interference is,

$$ d \sin \theta=m \lambda $$

Use the trigonometry, the angle made by the position on the screen with the horizontal is as follows.

$$ \tan \theta=\frac{y}{L} $$

If angles are very small, then

$$ \sin \theta=\tan \theta $$

Use the above equations,

$$ \begin{array}{l} \sin \theta=\frac{y}{L} \\ \frac{m \lambda}{d}=\frac{y}{L} \quad\left(\text { Since } \sin \theta=\frac{m \lambda}{d}\right) \end{array} $$

For adjacent fringes, the

$$ \Delta y=\frac{L \lambda \Delta m}{d} $$

Substitute the numerical values we get

$$ \begin{aligned} \Delta y &=\frac{(4.0 \mathrm{~m})\left(594 \times 10^{-9} \mathrm{~m}\right)(1)}{1.5 \times 10^{-3} \mathrm{~m}} \\ &=1.584 \times 10^{-3} \mathrm{~m} \end{aligned} $$