To determine the number of bright and dark bands observed between points P and Q in a double slit experiment, we can use the concept of path difference and the wavelength of the light used. The key idea here is that bright bands occur where the path difference is a multiple of the wavelength, while dark bands occur where the path difference is an odd multiple of half the wavelength.
Understanding Path Differences
In this scenario, we have two path differences:
- At point P: ΔdP = 7.5 x 10-6 m
- At point Q: ΔdQ = 1.8 x 10-6 m
Calculating the Range of Path Differences
The total range of path differences between points P and Q can be calculated by finding the difference between the two path differences:
Δdtotal = ΔdP - ΔdQ = (7.5 x 10-6 m) - (1.8 x 10-6 m) = 5.7 x 10-6 m
Finding the Number of Bands
Next, we need to determine how many wavelengths fit into this total path difference. The wavelength of the light used is given as λ = 6 x 10-7 m. We can find the number of wavelengths in the total path difference:
Number of wavelengths = Δdtotal / λ = (5.7 x 10-6 m) / (6 x 10-7 m) = 9.5
Interpreting the Results
Since the number of wavelengths is approximately 9.5, we can conclude that there are 9 complete wavelengths and a half wavelength in the path difference between points P and Q. This means:
- There will be 9 bright bands corresponding to the complete wavelengths.
- Additionally, there will be 9 dark bands corresponding to the half wavelengths.
Final Count of Bands
To summarize, between points P and Q, we can observe:
- 9 bright bands
- 9 dark bands
Thus, the total number of bands (both bright and dark) observed between points P and Q is 18. This illustrates how the interference pattern in a double slit experiment can be analyzed using path differences and the wavelength of light.
