In young's double slit experiment the separation `d` between the slits is `2mm`, the wavelength `lambda` of the light used is `5896 Å` and distance `D` between the screen and slits is `100 cm`. It is found that the angular width of the fringes is `0.20^(@)`. To increases the fringe angular width to `0.21^(@)`(with same `lambda` and `D`) the separtion between the slits needs to be changed to

Options

A. 2.1 mm
B. 1.9 mm
C. 1.8 mm
D. 1.7 mm

Explanation

To solve the problem, we need to find the new separation between the slits (d₂) that will increase the angular width of the fringes from 0.20° to 0.21° while keeping the wavelength (λ) and the distance to the screen (D) constant.

### Step-by-Step Solution:

1. **Understanding Angular Width**:
The angular width (ω) of the fringes in Young's double slit experiment is given by the formula:
\[ \omega = \frac{\lambda}{d} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( d \) is the separation between the slits.

2. **Setting Up the Equations**:
For the initial condition (ω₁ = 0.20° and d₁ = 2 mm):
\[ \omega_1 = \frac{\lambda}{d_1} \]
For the new condition (ω₂ = 0.21° and d₂ is what we need to find):
\[ \omega_2 = \frac{\lambda}{d_2} \]

3. **Relating the Two Conditions**:
Since the wavelength (λ) is constant, we can equate the two expressions:
\[ \omega_1 d_1 = \omega_2 d_2 \]

4. **Substituting Known Values**:
Substitute the known values into the equation:
\[ (0.20°)(2 \text{ mm}) = (0.21°)(d_2) \]

5. **Solving for d₂**:
Rearranging the equation to solve for d₂:
\[ d_2 = \frac{(0.20°)(2 \text{ mm})}{0.21°} \]
\[ d_2 = \frac{0.40 \text{ mm}}{0.21} \]
\[ d_2 \approx 1.90476 \text{ mm} \]

6. **Rounding the Answer**:
Rounding to two decimal places, we find:
\[ d_2 \approx 1.90 \text{ mm} \]

### Final Answer:
The new separation between the slits should be approximately **1.9 mm**.