As depicted in the figure, a U-shaped wire is situated in front of a concave mirror with a radius of curvature of 20 cm . Calculate the total length of the image.

Step-by-step solution

For the concave mirror, the focal length is f = - R 2 = - 20 2 = -10 cm . The U-shaped wire consists of three segments: two vertical and one horizontal. 1. For the right vertical segment: Object distance, u₁ = -30 cm . Using the mirror formula, 1 v₁ + 1 u₁ = 1 f 1 v₁ - 1 30 = - 1 10 1 v₁ = 1 30 - 1 10 = - 2 30 v₁ = -15 cm Magnification, m₁ = - v₁ u₁ = - -15 -30 = - 1 2 Length of its image, L₁ = |m₁| h_o = 1 2 10 = 5 cm . 2. For the left vertical segment: Object distance, u₂ = -(30 + 10) = -40 cm . 1 v₂ - 1 40 = - 1