A glowing electric light bulb placed 15 cm from a concave spherical mirror produces a real image 8.5 cm from the mirror.

Question

a.) If the light bulb is moved to a position 25 cm from the mirror, what is the position of the image?

b.) What are the magnifications of the first and final images?

Answer 1

1/F = 1/15 + 1/8.5; F = 15·8.5/(15 + 8.5) = 5.4255 cm

a.) 1/F = 1/d + 1/f; f = F·d/(d - F) = 5.4255·25/(25 - 5.4255) = 6.93cm

b.) h₁/h = f₁/d₁; h₂/h = f₂/d₂; m = h₂/h₁ = f₂d₁/(f₁d₂) = 6.93·15/(8.5·25) = 0.49