Solved Examples of Diffraction Through a Single Slit

📚 Quick Study Guide

• ✨ Single-slit diffraction occurs when a wave passes through a narrow slit, causing it to spread out.
• 📏 The angle $\theta$ to the minima (dark fringes) in the diffraction pattern is given by: $a \sin(\theta) = m \lambda$, where $a$ is the slit width, $\lambda$ is the wavelength of light, and $m$ is the order of the minimum ($m = 1, 2, 3,...$).
• 💡 The central maximum is twice as wide as the other secondary maxima.
• 🌊 The intensity of the diffraction pattern decreases as you move away from the central maximum.
• 📐 For small angles, $\sin(\theta) \approx \theta$, so the formula simplifies to $a \theta = m \lambda$.

🧪 Practice Quiz

1. A beam of monochromatic light with a wavelength of 500 nm is incident on a single slit of width 2 μm. What is the angle of the first minimum?
   1. A) 7.18°
   2. B) 14.48°
   3. C) 28.96°
   4. D) 0.25°
2. If the slit width is decreased, what happens to the width of the central maximum in a single-slit diffraction pattern?
   1. A) Decreases
   2. B) Increases
   3. C) Remains the same
   4. D) Disappears
3. Monochromatic light passes through a slit of width 0.1 mm and forms a diffraction pattern on a screen 2 m away. The width of the central maximum is 2 cm. What is the wavelength of the light?
   1. A) 400 nm
   2. B) 500 nm
   3. C) 600 nm
   4. D) 700 nm
4. In a single-slit diffraction experiment, the slit width is equal to the wavelength of the light. At what angle does the first minimum occur?
   1. A) 0°
   2. B) 30°
   3. C) 90°
   4. D) 60°
5. What happens to the diffraction pattern if white light is used instead of monochromatic light?
   1. A) No pattern is formed.
   2. B) A sharper pattern is formed.
   3. C) A colored pattern is formed.
   4. D) The pattern remains the same.
6. The second minimum in a single-slit diffraction pattern occurs at an angle of 45°. What is the ratio of the wavelength of light to the slit width ($\lambda/a$)?
   1. A) $\sqrt{2}$
   2. B) $\frac{\sqrt{2}}{2}$
   3. C) $\frac{1}{\sqrt{2}}$
   4. D) 2
7. How does increasing the wavelength of light affect the spacing between the minima in a single-slit diffraction pattern?
   1. A) Decreases the spacing
   2. B) Increases the spacing
   3. C) Does not affect the spacing
   4. D) Makes the pattern disappear