A concave mirror is a part of sphere of radius 20 cm, the focal length of concave mirror is :

Options

A. 10 cm
B. 20 cm
C. `-20cm`
D. `-10cm`

Answer

To find the focal length of a concave mirror that is part of a sphere with a radius of 20 cm, we can use the relationship between the focal length (f) and the radius of curvature (R) of the mirror. The formula is:

\[ f = \frac{R}{2} \]

**Step-by-step solution:**

1. **Identify the radius of curvature (R):**
The radius of curvature of the concave mirror is given as 20 cm.

2. **Apply the formula for focal length:**
We know that the focal length (f) is half of the radius of curvature (R). Therefore, we can write:
\[ f = \frac{R}{2} \]

3. **Substitute the value of R:**
Substitute R = 20 cm into the formula:
\[ f = \frac{20 \, \text{cm}}{2} \]

4. **Calculate the focal length:**
Now, perform the division:
\[ f = 10 \, \text{cm} \]

5. **Conclusion:**
The focal length of the concave mirror is 10 cm.

**Final Answer:**
The focal length of the concave mirror is 10 cm.

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