# Thomas Young's Double-Slit Experiment Thomas Young conducted this experiment in 1801, providing crucial evidence for the wave nature of light. The experiment demonstrates that when coherent light passes through two closely spaced slits, it diffracts and creates an interference pattern of bright and dark fringes on a screen. This phenomenon is a direct consequence of the nature of light. ## Experimental Setup The experimental setup consists of three main components: 1. **Coherent Light Source**: A single source of light (such as a laser, or sunlight passed through a single slit) is used to ensure the waves have a definite phase relationship. 2. **Double Slit**: The light is directed at a barrier with two narrow, closely spaced vertical slits ($S_1$ and $S_2$). These slits act as two separate, coherent sources of light. 3. **Screen**: A screen placed behind the slits displays the interference pattern, which consists of alternating bright fringes (maxima) and dark fringes (minima). Without interference, only two bright lines would be visible. ## Path Difference For a point P on the screen, the wave from slit $S_2$ travels a slightly longer distance than the wave from slit $S_1$. This difference in distance is called the **path difference**. The path difference determines whether the waves interfere constructively or destructively at point P. The formula for path difference is: $$\text{Path difference} = d \sin \theta$$ where: - $d$ is the distance between the slits - $\theta$ is the angle from the center of the slits to the point P on the screen ## Conditions for Interference The following conditions must be satisfied for clear interference fringes to be observed: | Interference Type | Condition on Path Difference | Formula | Result on Screen | | :---------------- | :------------------------------------------- | :------------------------------------------------ | :--------------- | | **Constructive** | Integer multiple of the wavelength ($\lambda$) | $d \sin \theta = m\lambda$ | Bright Fringe (Maxima) | | **Destructive** | Odd multiple of half the wavelength | $d \sin \theta = \left(m+\frac{1}{2}\right)\lambda$ | Dark Fringe (Minima) | *Where $m = 0, \pm 1, \pm 2, \ldots$ is the order of the fringe.* ## Position of Fringes and Fringe Spacing For small angles ($\theta$), we can use the approximation $\sin \theta \approx \tan \theta = \frac{y}{L}$, where $y$ is the distance from the central maximum on the screen and $L$ is the distance from the slits to the screen. **Position of Bright Fringes (Maxima):** $$y = m \frac{\lambda L}{d}$$ **Position of Dark Fringes (Minima):** $$y = \left(m+\frac{1}{2}\right) \frac{\lambda L}{d}$$ **Fringe Spacing ($\Delta y$):** The distance between two consecutive bright or dark fringes. $$\Delta y = \frac{\lambda L}{d}$$ The spacing is the same for both bright and dark fringes. This experiment also relates to the broader concept of .

18.1.3 Interference Of Light Waves | Diffraction And Interference | Physics 12