A convex lens of focal length 20 cm and a concave lens of focal...

Case I: Light is incident on the convex lens first.

The incident parallel beam converges towards the principal focus of the convex lens, which is at a distance of $20 \text{ cm}$ from it.

The concave lens is placed $10 \text{ cm}$ from the convex lens. The distance of the focus of the convex lens from the concave lens is $20 - 10 = 10 \text{ cm}$.

This point acts as a virtual object for the concave lens. Since the focal length of the concave lens is $10 \text{ cm}$, the emergent beam becomes parallel to the principal axis.

Using similar triangles, the diameter of the emergent beam $D_2$ is related to the incident beam diameter $D_1$ by:

$\dfrac{D_2}{D_1} = \dfrac{10}{20}$

$D_2 = 5.0 \times \dfrac{1}{2} = 2.5 \text{ mm}$

Case II: Light is incident on the concave lens first.

The incident parallel beam diverges from the principal focus of the concave lens, which is at a distance of $10 \text{ cm}$ in front of it.

The convex lens is placed $10 \text{ cm}$ behind the concave lens. The distance of the focus of the concave lens from the convex lens is $10 + 10 = 20 \text{ cm}$.

This point acts as a real object for the convex lens. Since the focal length of the convex lens is $20 \text{ cm}$, the emergent beam becomes parallel to the principal axis.

Using similar triangles, the diameter of the emergent beam $D_2$ is related to the incident beam diameter $D_1$ by:

$\dfrac{D_2}{D_1} = \dfrac{20}{10}$

$D_2 = 5.0 \times 2 = 10.0 \text{ mm} = 1.0 \text{ cm}$

Therefore, the possible values for the beam diameter of the emergent beam are $2.5 \text{ mm}$ and $1.0 \text{ cm}$.