Two coherent sources `S_1" and "S_2` produce interference fringes. If a thin mica plate is introduced in the path of light from `S_(1)` then the central maximum

Options

A. shift towards `S_2`
B. shift towards `S_1`
C. do not shift to any side
D. disappear

Answer

To solve the problem of how the introduction of a thin mica plate in the path of light from source \( S_1 \) affects the central maximum in an interference pattern produced by two coherent sources \( S_1 \) and \( S_2 \), we can follow these steps:

### Step 1: Understand the Interference Pattern
The interference pattern is formed due to the superposition of light waves from two coherent sources, \( S_1 \) and \( S_2 \). The central maximum occurs where the path difference between the two waves is zero.

**Hint:** Recall that the central maximum is the point of constructive interference where the path difference is zero.

### Step 2: Introduce the Mica Plate
When a thin mica plate is introduced in the path of light from \( S_1 \), it changes the optical path length of the light coming from that source. The optical path length is affected by the refractive index \( \mu \) of the mica and the thickness \( t \) of the plate.

**Hint:** Remember that the optical path length is given by \( \text{Optical Path Length} = \mu \cdot t \).

### Step 3: Calculate the Additional Path Difference
The introduction of the mica plate introduces an additional path difference given by:
\[ \Delta = (\mu - 1) \cdot t \]
This additional path difference shifts the effective position of the central maximum.

**Hint:** Consider how the additional path difference affects the existing path difference at the central maximum.

### Step 4: Analyze the Effect on the Central Maximum
Since the central maximum originally had a path difference of zero, the introduction of the mica plate means that the path difference is no longer zero. To restore the condition for the central maximum (path difference of zero), the position of the central maximum must shift.

**Hint:** The central maximum will shift towards the source that has the additional optical path length (in this case, \( S_1 \)).

### Step 5: Conclusion
Thus, the central maximum will shift towards \( S_1 \) because the additional optical path length introduced by the mica plate effectively increases the path length from \( S_1 \) relative to \( S_2 \).

**Final Answer:** The central maximum shifts towards \( S_1 \).