## **Step 1: Reducing Slit Width (D) with Constant Slit Distance (d)** When the **slit width (D is reduced** while keeping the **distance between the slits (d) constant**: - **Diffraction envelope widens**: The single-slit diffraction envelope becomes broader because the angular width is inversely proportional to D. - **Fringe visibility increases**: More fringes will fit under the central maximum of the envelope, and the fringes become sharper and more distinct. **Explanation:** The width of the central diffraction maximum is given by \[ \theta = \frac{\lambda}{D} \] So, reducing D increases θ, making the central bright fringe wider and more fringes visible. **Diagram:** ``` Wider envelope, more visible fringes | | | | | |----|----|----|----| ``` --- ## **Step 2: Reducing Distance Between Slits (d) with Constant Slit Width (D)** When the **distance between the slits (d) is reduced** while **slit width (D) remains constant**: - **Fringe separation increases**: The distance between adjacent bright fringes increases, making the fringes farther apart. - **Envelope remains same**: The overall diffraction envelope does not change since D is constant. **Explanation:** The fringe separation is given by \[ \Delta x = \frac{\lambda L}{d} \] So, reducing d increases Δx, making the bright and dark fringes more widely spaced. **Diagram:** ``` Fringes farther apart, same envelope width | | | | |-------|-------|-------| ``` --- ## **Final Answer Summary** - (i) **Reducing slit width (D):** Diffraction envelope widens, more and sharper fringes visible. - (ii) **Reducing slit distance (d):** Fringes become farther apart, envelope width unchanged. **Both effects can be visualized by how the pattern stretches and spreads on the screen.**

## **Step 1: Reducing Slit Width (D) with Constant Slit Distance (d)** When the **slit width (D) is reduced** while keeping the **distance between the slits (d) constant**: - **Diffraction envelope widens**: The single-slit diffraction pattern broadens as the angular width increases. - **Fringe visibility increases**: More fringes become visible under the central maximum, appearing sharper. **Explanation:** The width of the central diffraction maximum is defined by \[ \theta = \frac{\lambda}{D} \] Reducing D increases \(\theta\), resulting in a wider central bright fringe and more visible fringes. **Diagram:** ``` Wider envelope, more visible fringes | | | | | |----|----|----|----| ``` --- ## **Step 2: Reducing Distance Between Slits (d) with Constant Slit Width (D)** When the **distance between the slits (d) is reduced** while keeping **slit width (D) constant**: - **Fringe separation increases**: The distance between adjacent bright fringes becomes larger, leading to a wider spacing between them. - **Envelope remains the same**: The overall diffraction envelope does not change as D is held constant. **Explanation:** The fringe separation is given by \[ \Delta x = \frac{\lambda L}{d} \] Thus, reducing d increases \(\Delta x\), causing the bright and dark fringes to spread farther apart. **Diagram:** ``` Fringes farther apart, same envelope width | | | | |-------|-------|-------| ``` --- ## **Final Answer Summary** - (i) **Reducing slit width (D)**: Results in a wider diffraction envelope and more visible, sharper fringes. - (ii) **Reducing slit distance (d)**: Leads to increased fringe separation while the envelope width remains unchanged. Both effects illustrate how adjustments to slit dimensions influence the interference pattern observed on the screen.