The optical path difference between two identical light waves arriving at a point is 31.5 `lamda`, where `lamda` is the wavelength of light. The point is

Options

A. Bright
B. Dark
C. Alternatively bright and dark
D. Neither bright nor dark

Explanation

To solve the problem, we need to determine whether the point where two identical light waves arrive, with an optical path difference of 31.5 λ (lambda), will be a bright point, a dark point, or neither.

### Step-by-Step Solution:

1. **Understanding Optical Path Difference (OPD)**:
The optical path difference (OPD) is the difference in the distance traveled by two waves arriving at a point. It is given as 31.5 λ.

2. **Expressing OPD in Fractional Form**:
We can express 31.5 λ in a more manageable form.
\[ 31.5 \lambda = \frac{63}{2} \lambda \]
This shows that the OPD can be represented as a fraction of λ.

3. **Identifying Bright and Dark Points**:
- For constructive interference (bright point), the OPD must be an integer multiple of the wavelength (nλ, where n is an integer).
- For destructive interference (dark point), the OPD must be an odd multiple of half the wavelength \((n + \frac{1}{2})\lambda\), where n is an integer.

4. **Analyzing the Given OPD**:
The OPD we have is \(\frac{63}{2} \lambda\). Here, 63 is an odd number.
- Since 63 is odd, we can express it as:
\[ \frac{63}{2} \lambda = 31 \lambda + \frac{1}{2} \lambda \]
This indicates that the OPD corresponds to a condition for destructive interference.

5. **Conclusion**:
Since the OPD of 31.5 λ corresponds to an odd multiple of \(\frac{1}{2} \lambda\), the point will be a dark point.

### Final Answer:
The point is a dark point.