A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

Options

A. parabola
B. straight line
C. circle
D. hyperbola

Answer

To solve the question regarding the shape of the interference fringes formed in a Young's double slit experiment using a monochromatic source, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**: In a Young's double slit experiment, light from a monochromatic source passes through two closely spaced slits and creates an interference pattern on a screen placed at some distance.

2. **Identify the Nature of Interference**: The interference pattern results from the superposition of light waves emanating from the two slits. When these waves meet, they can interfere constructively (bright fringes) or destructively (dark fringes).

3. **Determine the Shape of the Fringes**: The interference fringes are typically observed as alternating bright and dark bands. The shape of these fringes can be analyzed mathematically.

4. **Mathematical Analysis**: The positions of the bright and dark fringes can be described using the path difference between the two waves reaching a point on the screen. The condition for constructive interference (bright fringes) is given by:
\[ d \sin \theta = n \lambda \]
where \(d\) is the distance between the slits, \(\theta\) is the angle of the fringe from the central maximum, \(n\) is an integer (0, 1, 2,...), and \(\lambda\) is the wavelength of the light.

5. **Shape Identification**: If we analyze the geometry of the situation, the bright fringes can be represented as hyperbolas in a coordinate system where the slits are the foci. This is because the path difference corresponds to a constant value for each fringe, which is characteristic of hyperbolic equations.

6. **Conclusion**: Therefore, the shape of the interference fringes formed on the screen in a Young's double slit experiment with a monochromatic source is a hyperbola.

### Final Answer:
The shape of the interference fringes formed on the screen is a hyperbola.

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