# Wave Optics: Interference and Diffraction

Physics I · Principles of Electromagnetism and Optics · https://tryals.app/learn/physics-i/wave-optics-interference-and-diffraction

## Young's Double-Slit & Diffraction

Shine light through two close slits and the screen shows stripes, places where light plus light equals **darkness**. Only waves can cancel.

**Young's double-slit** uses slits separated by $d$ to create distinct patterns:

| Fringe Type | Formula | Condition |
| --- | --- | --- |
| **Bright** | $d\sin\theta = m\lambda$ | $m = 0, \pm 1, \pm 2$ |
| **Dark** | $d\sin\theta = (m+\tfrac{1}{2})\lambda$ | $m = 0, \pm 1, \pm 2$ |

**Single-slit diffraction** uses slit width $a$ where dark fringes obey $a\sin\theta = m\lambda$.

**Diffraction grating** uses $N$ slits to give sharper maxima with resolution $R = mN$.

## Thin-Film & Resolution Limits

**Thin-film interference** combines path difference $\Delta = 2nt$ with reflection shifts at higher-$n$ boundaries, adding an extra $\lambda/2$ phase change.

| Reflection Shifts | Constructive Interference |
| --- | --- |
| **One shift** | $2nt = (m+\tfrac{1}{2})\lambda$ |
| **Zero or two shifts** | $2nt = m\lambda$ |

Telescope resolution is limited by diffraction: $\theta_{\min} = 1.22\lambda/D$.

**Common pitfall:** Interference never destroys energy. Dark fringes are matched by doubly-bright ones; energy is only redistributed, never lost.

## Practice questions

8 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. In a double-slit experiment you make the two slits **closer together**. What happens to the bright fringes on the screen?

A. They spread farther apart
B. They disappear, interference needs wide spacing
C. They stay put but get dimmer
D. They squeeze closer together

**Answer:** A. They spread farther apart

**Why:** The geometry is reciprocal: tighter slits throw a wider pattern ($\sin\theta = m\lambda/d$). This inverse relationship is the heart of diffraction, and the reason small things are hard to see with light: the finer the detail, the wider the light spreads.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/in-a-double-slit-experiment-you-make-the-two-slits-closer-together

### 2. Interference produces bright and dark fringes, with dark bands where two beams both deliver light. Does that mean energy is being destroyed?

A. No, because the dark fringes still carry energy that is simply not visible
B. No, the energy is redistributed rather than removed
C. Yes, destructive interference converts light energy into heat
D. Yes, but only for coherent sources, which is why interference requires them

**Answer:** B. No, the energy is redistributed rather than removed

**Why:** Interference moves energy around the screen. The dark fringes give up exactly what the bright ones gain, conservation holds over the pattern, not point by point.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/interference-produces-bright-and-dark-fringes-with-dark-bands-where

### 3. In Young's double-slit experiment, bright fringes occur where the path difference is a half-integer number of wavelengths.

**Answer:** False

**Why:** False. Whole-wavelength path differences arrive in phase and give the **bright** fringes; half-integer differences arrive antiphase and give the dark ones. Getting the condition the wrong way round inverts the entire pattern, and the fringe spacing $\lambda L/d$ is what turns it into a measurement of wavelength.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/in-youngs-double-slit-experiment-bright-fringes-occur-where-the

### 4. Double slit: $d = 0.1 mm$, $\lambda$ = 500 nm. What is the angle (in degrees) for the first bright fringe ($m=1)$? **Set the slider to your answer.**

**Answer:** 0.29 (within ±0.01)

**Why:** sin $\theta$ = mλ/$d = 500\times10$⁻⁹/10⁻⁴ = 0.005 → $\theta$ = $arcsin(0.005)$ $\approx 0.29$°.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/double-slit-d-0-1-mm-500-nm-what-is-the-angle-in-degrees

### 5. Match each wave optics phenomenon to its key equation.

**Answer:**

- Double-slit bright fringe → $d\sin\theta = m\lambda$
- Single-slit dark fringe → $a\sin\theta = m\lambda,\ m \ne 0$
- Thin-film constructive (in air) → $2nt = (m+\tfrac{1}{2})\lambda$
- Rayleigh resolution limit → $\theta \approx 1.22\,\lambda/D$

**Why:** Slits that are close together (separation d) give interference maxima; a single opening of width a gives diffraction minima; thin films add a half-wave flip on reflection; and Rayleigh’s criterion sets the smallest angle two sources can be apart and still be distinguished.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/match-each-wave-optics-phenomenon-to-its-key-equation

### 6. Which phenomena demonstrate the wave nature of light?

A. Rectilinear propagation (casting sharp shadows)
B. Polarization
C. Interference patterns
D. Diffraction

**Answer:** B. Polarization; C. Interference patterns; D. Diffraction

**Why:** Sharp shadows suggest particle behavior; interference, diffraction, and polarization are wave phenomena.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/which-phenomena-demonstrate-the-wave-nature-of-light

### 7. Complete the following passage by choosing the correct terms from the word bank.

**Answer:** When two waves interfere constructively, the resulting amplitude is **greater** than either individual amplitude. Destructive interference can produce **zero** amplitude.

**Why:** Constructive: amplitudes add. Destructive: amplitudes cancel (can reach zero).

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/complete-the-following-passage-by-choosing-the-correct-terms-from-the

### 8. Sort: double-slit interference or single-slit diffraction?

**Answer:**

- Double-slit: $d \sin\theta = m\lambda$ for bright fringes, Equally spaced bright fringes, Two narrow openings
- Single-slit diffraction: $a \sin\theta = m\lambda$ for dark fringes, Central maximum is twice as wide as others, One wide opening

**Why:** Double-slit produces equally spaced fringes; single-slit has a broad central peak.

Page: https://tryals.app/practice/physics-i/wave-optics-interference-and-diffraction/sort-double-slit-interference-or-single-slit-diffraction