A beam of light parallel to the principal axis of a concave and convex lens, first passes through the concave lens of focal length 0.5 m and then through the convex lens of focal length 1.75 m . If the lenses are placed 1.25 apart, which of the given statement is true?

Let the focal length of the concave lens be $f_1 = -0.5$ m and the focal length of the convex lens be $f_2 = 1.75$ m. The distance between the lenses is $d = 1.25$ m.

A beam of light parallel to the principal axis incident on the concave lens will appear to diverge from its focus, which is at a distance of $0.5$ m in front of the concave lens. Thus, the virtual object for the convex lens is located at a distance $u = -(d + |f_1|) = -(1.25 + 0.5) = -1.75$ m from the convex lens.

Using the lens formula for the convex lens: $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f_2}$.

Substituting the values: $\dfrac{1}{v} - \dfrac{1}{-1.75} = \dfrac{1}{1.75}$.

This simplifies to $\dfrac{1}{v} + \dfrac{1}{1.75} = \dfrac{1}{1.75}$, which gives $\dfrac{1}{v} = 0$.

Therefore, $v = \infty$. The emergent beam will be parallel to the principal axis.

Answer: The emergent beam will pass parallel to the principal axis.