Monochromatic light falls on two narrow slits that are 0.0190 mm apart. A first order fringe is 18 mm from the central line. The screen (back wall) is 0.600 m from the slits. What is the wavelength of the light?

Answer 1

We can use the equation for the fringe separation in a double-slit experiment to solve this problem:

$$y = m \frac{\lambda L}{s}$$

Here, y is the first order fringe distance from the central line, m is the order number, λ is the wavelength of the light, L is the distance between the slits and the screen, and s is the distance between the slits. Rearranging the equation to solve for λ, we get:

$$\lambda = \frac{y s}{m L}$$

Plugging in the given values, we can calculate the wavelength:

$$\lambda = \frac{18 \times 10^{-3}\,\text{m} \times 0.0190 \times 10^{-3}\,\text{m}}{1 \times 0.600\,\text{m}}$$

$$\lambda = \frac{3.42 \times 10^{-7}\,\text{m}^2}{0.600\,\text{m}}$$

$$\lambda = 5.7 \times 10^{-7}\,\text{m}$$

The wavelength of the light is approximately 570 nm.