**Introduction:**
A thin lens and a spherical mirror have a focal length of 15 cm each. We need to determine which combination of convex and concave lenses and mirrors would give us this focal length.

**Explanation:**
To understand why the correct answer is option 'A', let's consider the properties of convex and concave lenses and mirrors.

1. **Convex lens:** A convex lens is thicker in the middle and thinner at the edges. It converges light rays and forms real, inverted images when the object is placed beyond the focal point. The focal length of a convex lens is positive.

2. **Concave lens:** A concave lens is thinner in the middle and thicker at the edges. It diverges light rays and forms virtual, erect images. The focal length of a concave lens is negative.

3. **Convex mirror:** A convex mirror is curved outward, causing light rays to diverge. It forms virtual, erect images. The focal length of a convex mirror is negative.

4. **Concave mirror:** A concave mirror is curved inward, causing light rays to converge. It forms real, inverted images when the object is placed beyond the focal point. The focal length of a concave mirror is positive.

Given that both the lens and the mirror have a focal length of 15 cm, we can conclude the following:

- A convex lens and a convex mirror cannot have the same focal length. The focal length of a convex mirror is negative, while the focal length of a convex lens is positive.

- A concave lens and a convex mirror cannot have the same focal length. The focal length of a concave lens is negative, while the focal length of a convex mirror is negative.

- A concave lens and a concave mirror cannot have the same focal length. The focal length of a concave lens is negative, while the focal length of a concave mirror is positive.

Therefore, the only combination that satisfies the given condition is when both the lens and the mirror are convex. In this case, they will have the same focal length of 15 cm.

**Conclusion:**
The correct answer is option 'A' - Both the thin lens and the spherical mirror are convex.

Yes . Option A is correct.
EXPLANATION:- Both the lenses are convex because the focal length of convex lens or mirror is positive as it lies in the direction of incident rays .