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A stone in free fall covers distances $h_1$, $h_2$, $h_3$ in successive 5-second intervals. The correct relation is:
Distances in successive equal time intervals from rest are in the ratio of odd numbers: $1:3:5:7\ldots$
So $h_1 : h_2 : h_3 = 1 : 3 : 5$, i.e., $\mathbf{h_1 = \dfrac{h_2}{3} = \dfrac{h_3}{5}}$
Angular width $2\theta = \frac{2\lambda}{a} = 60^\circ = \frac{\pi}{3} \text{ rad}$.
$\frac{\lambda}{a} = \frac{\pi}{6} \implies \lambda = \frac{\pi}{6} \times 1 \ \mu\text{m}$.
Fringe width $\beta = \frac{\lambda D}{d} = 1 \text{ cm} = 10^{-2} \text{ m}$.
$d = \frac{\lambda D}{\beta} = \frac{(\pi/6 \times 10^{-6}) \times 0.5}{0.01} \approx 26.1 \ \mu\text{m}$. The closest option is $25 \ \mu\text{m}$.
PE Classification (ESC 2019):
| Category | Criteria | Treatment |
|---|---|---|
| Massive (High Risk) | Hemodynamic instability: SBP \(< 90 \text{ mmHg}\) or drop \(\geq 40 \text{ mmHg}\) \(> 15\) min | Systemic thrombolysis or surgical embolectomy |
| Submassive (Intermediate) | Hemodynamically stable + RV dysfunction or elevated troponin/BNP | Anticoagulation ยฑ consider thrombolysis |
| Low Risk | Hemodynamically stable, no RV dysfunction | Anticoagulation (DOAC or heparin) |
Absolute contraindications to thrombolysis include: prior intracranial hemorrhage, active bleeding, recent surgery \(< 3\) weeks. If contraindicated โ surgical embolectomy or catheter-directed thrombolysis.
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