Given:
- Wavelength of green light (λ) = 5303 Å = 530.3 nm
- Slit separation (d) = 19.44 µm = 19.44 × 10⁻⁶ m
- Slit width (a) = 4.05 µm = 4.05 × 10⁻⁶ m

To find: Number of bright fringes between the first and second diffraction minima

Formula used:
- Distance between adjacent bright fringes (y) = λD/d, where D is the distance between the double slit and the screen
- Distance from the central maximum to the first minimum (y₁) = λD/a

Explanation:
- The double-slit experiment is a classic experiment in which light is passed through two narrow slits and the resulting interference pattern is observed on a screen.
- The interference pattern is a result of the superposition of the waves from the two slits.
- The bright fringes occur where the waves from the two slits reinforce each other, and the dark fringes occur where they cancel each other out.
- The distance between adjacent bright fringes is given by the formula y = λD/d, where D is the distance between the double slit and the screen.
- The distance from the central maximum to the first minimum is given by the formula y₁ = λD/a.

Solution:
- The distance from the central maximum to the first minimum is y₁ = λD/a = (530.3 × 10⁻⁹ m)(1.0 m)/4.05 × 10⁻⁶ m = 0.131 m
- The distance between adjacent bright fringes is y = λD/d = (530.3 × 10⁻⁹ m)(1.0 m)/19.44 × 10⁻⁶ m = 0.027 m
- The number of bright fringes between the first and second diffraction minima is (y₂ - y₁)/y, where y₂ is the distance from the central maximum to the second minimum.
- The distance from the central maximum to the second minimum can be found using the formula y₂ = 2y₁, since the distance between the first and second minima is twice the distance from the central maximum to the first minimum.
- Therefore, y₂ = 2y₁ = 2(0.131 m) = 0.262 m
- The number of bright fringes between the first and second diffraction minima is (y₂ - y₁)/y = (0.262 m - 0.131 m)/(0.027 m) = 4.85.
- Since the number of fringes must be a whole number, the answer is 5, which corresponds to option (B).

Therefore, the correct answer is option (B), i.e., 5.