Question 11

Step 1: Identify the formula for first minimum in single slit diffraction. $a \sin \theta = \lambda$ For small angles, $\sin \theta \approx \theta$ (in radians), so $\lambda \approx a \theta$.

Step 2: Express the fractional error. $\frac{\Delta \lambda}{\lambda} = \frac{\Delta a}{a} + \frac{\Delta (\sin \theta)}{\sin \theta}$ For small angles $\frac{\Delta (\sin \theta)}{\sin \theta} \approx \frac{\Delta \theta}{\theta}$.

Step 3: Calculate individual fractional errors. Width error: $\frac{\Delta a}{a} = \frac{0.002}{0.016} = \frac{1}{8} = 0.125$

Angle error: Convert everything to the same unit (minutes or degrees). $\theta = 2^{\circ} = 120'$ $\Delta \theta = 40'$ $\frac{\Delta \theta}{\theta} = \frac{40'}{120'} = \frac{1}{3} \approx 0.3333$

Step 4: Calculate total fractional error. $\frac{\Delta \lambda}{\lambda} = 0.125 + 0.3333 = 0.4583$ Rounding to two decimal places as per instruction: 0.46.

Final Answer: 0.46