The inside portion of part of a hollow metal sphere of diameter 20cm is polished. The portion will therefore form a?

1. Analyze the question

We are given a hollow metal sphere with a diameter of 20 cm. We are told that the inside portion of this sphere is polished to act as a mirror. We need to determine the type of mirror formed and its focal length.

2. Explain the concept

• Mirror Type: A mirror is classified based on its reflecting surface. If the reflecting surface is the inner (caved-in) part of a sphere, it is a concave mirror. If the reflecting surface is the outer (bulging) part, it is a convex mirror. Since the inside is polished, it is a concave mirror.
• Focal Length ($f$): The focal length of a spherical mirror is exactly half of its radius of curvature ($R$). • Formula: $f = \frac{R}{2}$ • The radius of curvature ($R$) is half of the diameter ($D$). • Formula: $R = \frac{D}{2}$

3. Show the solution

• Step 1: Find the radius of curvature ($R$). Given the diameter ($D$) = 20 cm. $R = \frac{D}{2} = \frac{20\text{ cm}}{2} = 10\text{ cm}$.

• Step 2: Calculate the focal length ($f$). Using the relationship $f = \frac{R}{2}$: $f = \frac{10\text{ cm}}{2} = 5\text{ cm}$.

• Step 3: Conclusion. Since the inside is polished, it is a concave mirror with a focal length of 5 cm.

4. Identify the answer

Comparing our result to the given options, the correct choice is A.

5. Exam Tip

Always remember the "C-C-C" rule for mirrors: Concave mirrors have Caved-in reflecting surfaces. Also, never confuse the radius of curvature with the focal length; always check if the question gives you the diameter or the radius before dividing by 2!