In a double-slit interference pattern, the position of the dark lines (or fringes) on the screen is given by the condition for destructive interference. This can be described using the formula:
y=‌Here:
-
y is the position of the dark fringe on the screen.
-
m is an integer representing the order of the dark fringe
(0,1,2,...).
-
λ is the wavelength of the monochromatic light.
- D is the distance between the screen and the slits.
-
d is the separation between the two slits.
The separation between the adjacent dark fringes (dark lines) is given by the distance
∆y between two consecutive dark fringes:
∆y=‌ From the above equation, we can see that
∆y (the separation between the dark lines) will increase if:
1. We increase the wavelength
λ of the light.
2. We increase the distance D between the screen and the slits.
3. We decrease the slit separation
d.
Now, considering the options provided:
Option A: Decreasing the distance between the screen and the slits would decrease
∆y, thus the separation between the dark lines would decrease.
Option B: Increasing the distance between the slits would decrease
∆y, thus the separation between the dark lines would decrease.
Option C: Using monochromatic light of a longer wavelength will increase
∆y, thus the separation between the dark lines would increase.
Option D: Using monochromatic light of higher frequency will decrease the wavelength, because wavelength and frequency are inversely proportional to each other. This would decrease
∆y, thus the separation between the dark lines would decrease.
Therefore, the correct answer is:
Option C: Using monochromatic light of a longer wavelength