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, ...).

- $$\lambda$$ is the wavelength of the monochromatic light.

- $$\mathrm{D}$$ 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 $$\Delta y$$ between two consecutive dark fringes:

$$\Delta y = \frac{\lambda D}{d}$$

From the above equation, we can see that $$\Delta y$$ (the separation between the dark lines) will increase if:

1. We increase the wavelength $$\lambda$$ of the light.

2. We increase the distance $$\mathrm{D}$$ 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 $$\Delta y$$, thus the separation between the dark lines would decrease.

Option B: Increasing the distance between the slits would decrease $$\Delta y$$, thus the separation between the dark lines would decrease.

Option C: Using monochromatic light of a longer wavelength will increase $$\Delta y$$, 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 $$\Delta y$$, thus the separation between the dark lines would decrease.

Therefore, the correct answer is:

Option C: Using monochromatic light of a longer wavelength

Wave Optics

Continue this paper

Similar Wave Optics PYQs

More practice from this question