A double-slit apparatus is used to observe an interference patten projected on a screen from a stationary light source. If the light source is instead moved toward the double slits at constant speed along the axis of symmetry. What will be observed on the screen ?

Options

A. The interference patten will remain unchanged
B. The fringes will move father apart to a new fixed direction.
C. the fringes will move closer together to a new fixed distance.
D. The fringes will continue to move further and farther apart as the source is brought closer.

Answer

To solve the problem, we need to analyze the situation of a double-slit interference pattern when the light source is moved toward the slits at a constant speed. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Double-Slit Experiment
In a double-slit experiment, light from a coherent source passes through two closely spaced slits, creating an interference pattern of bright and dark fringes on a screen due to constructive and destructive interference.

### Step 2: Identify the Parameters
- Let \( \lambda \) be the wavelength of the light.
- Let \( D \) be the distance from the slits to the screen.
- Let \( d \) be the distance between the two slits.

### Step 3: Analyze the Effect of Moving the Light Source
When the light source is moved toward the double slits:
- The distance \( D \) (from the slits to the screen) remains constant.
- The distance \( d \) (between the slits) also remains constant.
- The wavelength \( \lambda \) of the light does not change.

### Step 4: Determine Path Difference
The path difference between the light rays coming from the two slits to any point on the screen is given by the difference in distances traveled by the two rays. As the source moves toward the slits, the path difference at any point on the screen remains unchanged because both rays are still traveling the same distance to reach the screen.

### Step 5: Fringe Width Calculation
The fringe width \( \beta \) of the interference pattern is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
Since \( \lambda \), \( D \), and \( d \) remain constant, the fringe width \( \beta \) does not change.

### Step 6: Conclusion
As a result, even though the light source is moved toward the double slits at a constant speed, the interference pattern on the screen remains unchanged. The positions of the bright and dark fringes do not shift, and the overall pattern remains the same.

### Final Answer
When the light source is moved toward the double slits at constant speed, the interference pattern observed on the screen will remain unchanged.

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