Solved Examples of Interference Patterns in Double Slit Experiments

📚 Quick Study Guide

• ⚛️ The double-slit experiment demonstrates the wave-particle duality of light and matter.
• 🌊 Constructive interference occurs when the path difference between the waves from the two slits is an integer multiple of the wavelength ($d \sin{\theta} = m\lambda$, where $m = 0, 1, 2, ...$).
• 🌑 Destructive interference occurs when the path difference is a half-integer multiple of the wavelength ($d \sin{\theta} = (m + \frac{1}{2})\lambda$, where $m = 0, 1, 2, ...$).
• 📏 The fringe spacing ($\Delta y$) on the screen is given by $\Delta y = \frac{\lambda L}{d}$, where $\lambda$ is the wavelength, $L$ is the distance to the screen, and $d$ is the slit separation.
• 💡 Key parameters to consider are wavelength ($\lambda$), slit separation ($d$), distance to the screen ($L$), and the order of the fringe ($m$).

🧪 Practice Quiz

1. In a double-slit experiment, the slit separation is $0.2 \text{ mm}$ and the distance to the screen is $1 \text{ m}$. If the wavelength of light used is $500 \text{ nm}$, what is the fringe spacing?

   1. $2.5 \text{ mm}$
   2. $5.0 \text{ mm}$
   3. $1.0 \text{ mm}$
   4. $0.5 \text{ mm}$

2. For constructive interference to occur at an angle of $30^\circ$ in a double-slit experiment with a slit separation of $1.0 \mu\text{m}$, what wavelength of light should be used for the first-order maximum ($m=1$)?

   1. $250 \text{ nm}$
   2. $500 \text{ nm}$
   3. $750 \text{ nm}$
   4. $1000 \text{ nm}$

3. In a double-slit experiment, if the distance to the screen is doubled, what happens to the fringe spacing?

   1. It is halved.
   2. It remains the same.
   3. It is doubled.
   4. It is quadrupled.

4. If the slit separation in a double-slit experiment is decreased, what happens to the fringe spacing?

   1. It decreases.
   2. It increases.
   3. It remains the same.
   4. It becomes zero.

5. What happens to the interference pattern if white light is used instead of monochromatic light?

   1. The fringes become sharper.
   2. The fringes disappear.
   3. Colored fringes are observed.
   4. Only a central bright fringe is observed.

6. In a double-slit experiment, the third-order bright fringe is observed at an angle of $10^\circ$. If the wavelength of light is $600 \text{ nm}$, what is the slit separation?

   1. $1.04 \mu\text{m}$
   2. $10.4 \mu\text{m}$
   3. $104 \mu\text{m}$
   4. $1040 \mu\text{m}$

7. Two slits are separated by $0.1 \text{ mm}$. If the distance to the screen is $2 \text{ m}$ and the wavelength of light is $600 \text{ nm}$, what is the distance between the central bright fringe and the first dark fringe?

   1. $3 \text{ mm}$
   2. $6 \text{ mm}$
   3. $9 \text{ mm}$
   4. $12 \text{ mm}$