Question

The lens and mirror in the figure below are separated by 1.00 m and have focal lengths of +79.9 cm and -49.6 cm, respectively. If an object is placed 1.00 m to the left of the lens, where will the final image be located? q3 = cm State whether the image is upright or inverted, upright. inverted. Determine the overall magnification.

Answer 1

For a convex lens, we have

object distance, d₀ = 1 m

focal length, f₁ = +79.9 cm = 0.799 m

using a lens formula,

1 / d₀ + 1 / d_i = 1 / f₁

1 / d_i = 1 / (0.799 m) - 1 / (1 m)

d_i = 3.97 m

For a convex mirror, we have

object distance, d₀ = 2 m

focal length, f₂ = -49.6 cm = -0.496 m

using a mirror formula,

1 / d₀ + 1 / d_i = 1 / f₁

1 / d_i = 1 / (-0.496 m) - 1 / (2 m)

d_i = - 0.397 m

The final image will be located at a distance which given as :

q₃ = q₁ + q₂ $\Rightarrow$ (3.97 m) + (-0.397 m)

q₃ = 3.57 m

The image will be upright.

The overall magnification is given as :

m = - (3.57 m) / (2)

m = -1.78