Question

Monochromatic light is used to illuminate a pair of narrow slits 0.3 mm apart and the interference pattern is observed on a source 0.91 mm away. The second dark band appears 3.0 mm from the centre. What is the wavelength in metres?

Answer 1

QUESTION:

Monochromatic light is used to illuminate a pair of narrow slits $d = 0.3$ mm apart and the interference pattern is observed on a source $l = 0.91$ m away. The second dark band appears 3.0 mm from the centre. What is the wavelength in metres?

SOLUTION:

The spacing $\Delta x$ of the fringes at a distance $l$ from the slits is given by

$$\Delta x = \frac{l\lambda}{d}$$

As it can be seen from a picture above, the spacing between interference fringes is equal to the

$$\frac{3.0}{2} = 1.5 \text{ mm}$$

So

$$\lambda = \frac{\Delta x \cdot d}{l}$$ $$\lambda = \frac{1.5 \cdot 10^{-3} \cdot 0.3 \cdot 10^{-3}}{0.91} = 495 \cdot 10^{-9} \text{ m} = 495 \text{ nm}$$

ANSWER:

495·10⁻⁹ meters