1. Condition for bright fringes in YDSE

   Bright fringes occur when the path difference satisfies $d\sin\theta = m\lambda,$ where $m=0, \pm 1, \pm 2, \dots$

2. Given data

   $d = 0.320\text{ mm} = 3.20\times 10^{-4}\text{ m}$ $\lambda = 500\text{ nm} = 5.00\times 10^{-7}\text{ m}$

3. Angular range

   We need all bright fringes for $-30^\circ \le \theta \le 30^\circ.$

   Since $\sin 30^\circ = \frac{1}{2},$ the condition becomes $|\sin\theta| \le \frac{1}{2}.$

   So allowed $m$ must satisfy $\left|\frac{m\lambda}{d}\right| \le \frac{1}{2}.$

4. Find maximum order

   $|m| \le \frac{d}{2\lambda}$

   Substitute values: $\frac{d}{2\lambda} = \frac{3.20\times 10^{-4}}{2\times 5.00\times 10^{-7}}$

   $= \frac{3.20\times 10^{-4}}{1.00\times 10^{-6}} = 320$

   Thus, $m = -320, -319, \dots, -1, 0, 1, \dots, 319, 320.$

5. Count total bright fringes

   Number of integers from $-320$ to $320$ inclusive is $320 + 320 + 1 = 641.$

6. Check options

   • A: 640 ❌
   • B: 320 ❌
   • C: 321 ❌
   • D: 641 ✅

Therefore, the correct answer is D.