A spherical mirror and a thin spherical lens each have a focal length of `- 15 cm`. The mirror and lens are likely to be

Options

A. both concave
B. both convex
C. the mirror is concave and the lens is convex
D. the mirror is convex, but the lens is concave

Answer

To determine the nature of a spherical mirror and a thin spherical lens, both having a focal length of `-15 cm`, we can follow these steps:

### Step 1: Understand the Sign Convention
In optics, the sign of the focal length helps us identify the type of mirror or lens.
- For mirrors:
- A **concave mirror** has a **negative focal length**.
- A **convex mirror** has a **positive focal length**.

- For lenses:
- A **concave lens** has a **negative focal length**.
- A **convex lens** has a **positive focal length**.

### Step 2: Analyze the Given Focal Length
The problem states that the focal length for both the mirror and the lens is `-15 cm`.

### Step 3: Determine the Type of Mirror
Since the focal length is negative, we can conclude:
- The mirror must be a **concave mirror** because it has a negative focal length.

### Step 4: Determine the Type of Lens
Similarly, since the focal length is also negative for the lens:
- The lens must be a **concave lens** because it has a negative focal length.

### Conclusion
Both the spherical mirror and the thin spherical lens are concave.

### Summary of the Solution
- The mirror is a **concave mirror** (negative focal length).
- The lens is a **concave lens** (negative focal length).

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