When two coherent sources interact with each other, there will be production of alternate bright and dark fringes on the screen . Young's double-slit experiment domonstrates the idea of making two coherent sources. For better visibility, one has to choose proper amplitude for the sources. The phenomena is good enough to satisfy the conservation of energy principle. The pattern formed in YDSE is of uniform thickness and is nicely placed on a long distance screen.
For better visibility of fringe pattern

Options

A. amplitude of the sources are equal
B. the width of the slits should not be equal
C. dark should be the darkest and bright should be the brightest
D. the widths should be same

Explanation

To solve the problem regarding the visibility of fringe patterns in Young's double-slit experiment (YDSE), we will analyze the conditions necessary for achieving better visibility of the interference pattern.

### Step-by-Step Solution:

**Step 1: Understand the Concept of Coherent Sources**
- Coherent sources are sources that emit waves with a constant phase difference. In YDSE, two coherent sources are created by splitting a single wavefront, ensuring that the waves maintain a fixed phase relationship.

**Hint 1:** Coherent sources are crucial for producing a stable interference pattern.

**Step 2: Recognize the Importance of Amplitude**
- The amplitude of the waves from the two sources affects the intensity of the bright and dark fringes. For better visibility, the amplitudes of the two sources should be equal. This ensures that the maximum intensity is significantly higher than the minimum intensity.

**Hint 2:** Equal amplitudes lead to a clearer distinction between bright and dark fringes.

**Step 3: Calculate Maximum and Minimum Intensities**
- The intensity of the bright fringe (I_max) can be calculated using the formula:
\[ I_{max} = (A_1 + A_2)^2 = (A + A)^2 = (2A)^2 = 4A^2 \]
The intensity of the dark fringe (I_min) is given by:
\[ I_{min} = (A_1 - A_2)^2 = (A - A)^2 = 0 \]
This shows that the maximum intensity is four times the intensity of the individual sources when they are equal.

**Hint 3:** Knowing the formulas for maximum and minimum intensity helps in understanding the visibility of fringes.

**Step 4: Analyze the Visibility Condition**
- For better visibility of the fringe pattern, the difference between the maximum and minimum intensities should be large. If the minimum intensity is zero (complete darkness), the contrast between the bright and dark fringes is maximized.

**Hint 4:** A large difference in intensity between bright and dark fringes enhances visibility.

**Step 5: Consider the Width of the Slits**
- The width of the slits should be the same to ensure that the light passing through both slits has the same amplitude. This uniformity contributes to the clarity of the interference pattern.

**Hint 5:** Equal slit widths ensure consistent wavefronts and enhance fringe visibility.

**Step 6: Conclusion**
- For better visibility of the fringe pattern in Young's double-slit experiment, the following conditions should be met:
1. The amplitudes of the two coherent sources must be equal.
2. The width of the slits should be the same.
3. The intensity difference between maxima and minima should be significant.

**Final Answer:** To achieve better visibility of the fringe pattern in YDSE, ensure that the amplitudes of the sources are equal and the slit widths are the same.