Final answer:
The path difference in a diffraction grating can be calculated using the formula: path difference = distance between slits * sin(angle of diffraction). In this case, the path difference is approximately 0.0000022 m.
Step-by-step explanation:
The path difference in a diffraction grating can be calculated using the formula:
Path difference = distance between slits * sin(angle of diffraction)
In this case, the distance between the slits is 0.50 mm (or 0.0005 m) and the angle of diffraction is 0.25°. Plugging these values into the formula:
Path difference = 0.0005 * sin(0.25°)
Using a scientific calculator, we can get the value of the sine of 0.25° which is approximately 0.0043637. Multiplying this by 0.0005, we get a path difference of approximately 0.0000022 m.