A

Step 1: Calculate the force on the electron.
The force acting on the electron due to the electric field is given by:
$$ F = eE $$
where:
- $e$ = charge of the electron = $1.6 \times 10^{-19} \text{ C}$
- $E$ = electric field = $91 \times 10^{-6} \text{ V/m}$

Substituting the values:
$$ F = (1.6 \times 10^{-19}) (91 \times 10^{-6}) = 1.4576 \times 10^{-24} \text{ N} $$

Step 2: Calculate the acceleration of the electron.
Using Newton’s second law:
$$ F = ma $$
where:
- $m$ = mass of the electron = $9.1 \times 10^{-31} \text{ kg}$
Rearranging gives:
$$ a = \frac{F}{m} = \frac{1.4576 \times 10^{-24}}{9.1 \times 10^{-31}} = 1.6066 \times 10^{6} \text{ m/s}^2 $$

Step 3: Calculate the time the electron spends in the electric field.
The time ($t$) the electron spends in the field while traveling the length of the plates can be calculated as:
$$ t = \frac{\lambda}{v_0} = \frac{1}{4 \times 10^3} = 2.5 \times 10^{-4} \text{ s} $$

Step 4: Calculate the vertical displacement of the electron.
The vertical displacement ($y$) can be calculated using the equation:
$$ y = \frac{1}{2} a t^2 $$
Substituting the known values:
$$ y = \frac{1}{2} (1.6066 \times 10^{6}) (2.5 \times 10^{-4})^2 = 0.0251 \text{ m} $$

Step 5: Calculate the angle of deviation.
The angle ($\theta$) of deviation can be calculated using:
$$ \tan(\theta) = \frac{y}{\lambda} $$
Substituting the known values:
$$ \tan(\theta) = \frac{0.0251}{1} $$
Thus:
$$ \theta = \tan^{-1}(0.0251) \approx 0.0251 ext{ radians} \approx 1.44^{\circ} $$

Therefore, the angle of deviation is approximately $1.44^{\circ}$. The final answer is thus Option A.