If the radius of curvature of a concave mirror is 100 cm, what is its focal length?

Think it through first, then pick an option.

a − 2 m
b − 0.5 m
c + 0.5 m
d + 2 m

Answer and explanation

Correct answer: c + 0.5 m

f = r/2 = 100 cm ÷ 2 = 50 cm = 0.5 m. In the book the focal length is the distance from the pole to the focus, so it is the positive value 0.5 m; 2 m comes from multiplying r by 2 instead of halving it.

Why the other options are wrong

a − 2 m: This is not the answer: f = r/2 = 100 cm ÷ 2 = 50 cm = 0.5 m. In the book the focal length is the distance from the pole to the focus, so it is the positive value 0.5 m; 2 m comes from multiplying r by 2 instead of halving it.
b − 0.5 m: This is not the answer: f = r/2 = 100 cm ÷ 2 = 50 cm = 0.5 m. In the book the focal length is the distance from the pole to the focus, so it is the positive value 0.5 m; 2 m comes from multiplying r by 2 instead of halving it.
d + 2 m: This is not the answer: f = r/2 = 100 cm ÷ 2 = 50 cm = 0.5 m. In the book the focal length is the distance from the pole to the focus, so it is the positive value 0.5 m; 2 m comes from multiplying r by 2 instead of halving it.