S is the size of the slit, d is the separation between the slits and D is the distance of slits from a plane where Young's double slit interference pattern is being observed . If `lamda` be the wavelength of light, then for sharp fringes, the essential conditional is

Options

A. `S/Dlt(lamda)/d`
B. `S/Dgt (lamda)/d`
C. `S lamdalt dD`
D. `SD gt lamdad`

Explanation

To solve the problem regarding the conditions for sharp fringes in Young's Double Slit Experiment (YDSE), we need to analyze the relationship between the slit size (S), the separation between the slits (d), the distance from the slits to the observation plane (D), and the wavelength of light (λ).

### Step-by-Step Solution:

1. **Understanding Fringe Width**:
The fringe width (β) in YDSE is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- λ is the wavelength of light,
- D is the distance from the slits to the screen,
- d is the distance between the slits.

2. **Condition for Sharp Fringes**:
For sharp and clear fringes to be observed, the size of the slit (S) must be less than the fringe width (β). This is because if the slit size is too large, it will cause diffraction that can blur the fringes.

3. **Setting Up the Inequality**:
To ensure sharp fringes, we can express this condition mathematically:
\[ S < \beta \]
Substituting the expression for fringe width, we have:
\[ S < \frac{\lambda D}{d} \]

4. **Rearranging the Inequality**:
Rearranging the inequality gives:
\[ \frac{S \cdot d}{D} < \lambda \]
This means that the ratio of the slit size to the distance between the slits, when multiplied by the distance from the slits to the screen, must be less than the wavelength of light.

5. **Conclusion**:
Thus, the essential condition for sharp fringes in Young's Double Slit Experiment is:
\[ S < \frac{\lambda D}{d} \]

### Final Answer:
The essential condition for sharp fringes in Young's Double Slit Experiment is:
\[ S < \frac{\lambda D}{d} \]