Question 28: Wave Optics

Question

Two narrow parallel slits illuminated by a coherent monochromatic light produces an interference pattern on a screen
placed at a distance $$\mathrm{D}$$ from the slits. The separation between the dark lines of the interference pattern can be increased by

Accepted Answer

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:
$$y = \frac{(m + \frac{1}{2}) \lambda D}{d}$$
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

Answer

decreasing the distance between the screen and the slits

Answer

increasing the distance between the slits

Answer

using monochromatic light of a longer wavelength

Answer

using monochromatic light of higher frequency

Wave Optics

Two narrow parallel slits illuminated by a coherent monochromatic light produces an interference pattern on a screen placed at a distance $\mathrm{D}$ from the slits. The separation between the dark lines of the interference pattern can be increased by

Choose the correct answer: