In Young's double slit experiment, slits are arranged in such a way that besides central bright fringes, there is only one bright fringe on either side of it. Slit separation d for the given condition cannot be (if `lamda` is wavelength of the light used):

Options

A. `lamda`
B. `lamda//2`
C. `2lamda`
D. `3lamda//2`

Explanation

To solve the problem, we need to analyze the conditions under which only one bright fringe appears on either side of the central bright fringe in Young's double slit experiment.

### Step-by-Step Solution:

1. **Understanding the Condition**:
In Young's double slit experiment, bright fringes occur at positions where the path difference between the light from the two slits is an integer multiple of the wavelength (λ). The condition for maxima (bright fringes) is given by:
\[ d \sin \theta = n \lambda \]
where \( d \) is the slit separation, \( \theta \) is the angle of the fringe from the central maximum, and \( n \) is the order of the fringe (0 for central, ±1 for the first order, etc.).

2. **Given Condition**:
We are given that there is only one bright fringe on either side of the central maximum. This means that the first order maxima (n = ±1) are the only fringes visible.

3. **Finding the Maximum Path Difference**:
For the first order maximum (n = 1), the path difference is:
\[ d \sin \theta = \lambda \]
For the second order maximum (n = 2), the path difference would be:
\[ d \sin \theta = 2 \lambda \]
Since there is only one bright fringe on either side, the second order maximum must not exist. This implies that:
\[ d \sin \theta < 2 \lambda \]

4. **Calculating the Maximum Value of d**:
The maximum value of \( \sin \theta \) is 1 (which occurs at \( \theta = 90^\circ \)). Thus, the condition becomes:
\[ d < 2 \lambda \]
However, for the first order maximum to be visible, we also have:
\[ d \sin \theta \geq \lambda \]
This indicates:
\[ d \geq \lambda \]

5. **Combining the Conditions**:
Therefore, we have:
\[ \lambda \leq d < 2 \lambda \]
This means \( d \) can take values between \( \lambda \) and \( 2\lambda \).

6. **Conclusion**:
The slit separation \( d \) cannot be less than \( \lambda \) because then there would be more than one bright fringe on either side of the central maximum. Thus, the answer to the question is that \( d \) cannot be less than \( \lambda \).

### Final Answer:
The slit separation \( d \) for the given condition cannot be less than \( \lambda \).