In Young's double slit experiment, the angular separation of the fringes (θ) is given by :

$$\theta = \frac{m\lambda}{d}$$

where m is the fringe order, λ is the wavelength of the light, and d is the distance between the slits.

Now, let's analyze both statements:

Statement I: If the screen is moved away from the plane of the slits, the angular separation of the fringes remains constant.

This statement is true because the angular separation of the fringes (θ) does not depend on the distance between the screen and the slits. It only depends on the fringe order (m), the wavelength of the light (λ), and the distance between the slits (d).

Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.

This statement is false because if the wavelength (λ) increases, the angular separation of the fringes (θ) also increases according to the formula :

$$\theta = \frac{m\lambda}{d}$$

So, the correct answer is :

Option B: Statement I is true but Statement II is false.