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

Analyze the question: A hollow sphere has a diameter of 20 cm, so its radius is 10 cm. The inside surface is polished, so light reflects from the inner, curved-inward surface.

Concept:

• A spherical mirror whose reflecting surface curves inward (like the inside of a bowl) is a concave mirror.
• The radius of curvature (R) of the mirror equals the radius of the sphere.
• The focal length is half the radius of curvature: f = R/2

Solution:

1. Diameter = 20 cm, so radius R = 20 ÷ 2 = 10 cm.
2. The inside is polished, so it forms a concave mirror.
3. f = R/2 = 10/2 = 5 cm.

So the polished inner portion is a concave mirror of focal length 5 cm.

Checking the options:

• A. Concave, 5 cm ✔
• B. Concave, 10 cm ✘ (this mistakes the radius for the focal length)
• C and D. Convex ✘ (a convex mirror would need the outside surface polished)

Tip: Remember "Inside = Cave": the inside of a sphere gives a concave mirror. Always use f = R/2, and don't confuse the diameter, radius, and focal length. Diameter → halve it to get R → halve again to get f. So f = diameter/4 here: 20/4 = 5 cm.