Question

A car uses a convex mirror of curvature 1.2 m as its rear-view mirror. A minibus of cross-section 2.2 m × 2.2 m is 6.6 m away from the mirror. Estimate the image size.

Answer 1

For a convex mirror,
f = `"R"/2=1.2/2` = +0.6m
Given that, a minibus, approximately the shape of square is at distance of 6.6 m from the mirror.
i.e., u = – 6.6 m

From mirror formula,
`1/"f"=1/"v"+1/"u"`

∴ `1/"v"=1/"f"-1/"u"`

= `1/0.6-1/((-6.6))`

= `7.2/3.96=20/11`

∴ v = 0.55 m
As lateral magnification,
m = `"h"_2/"h"_1=-"v"/"u"`

∴ `"h"_2/((2.2))=-((0.55))/((-6.6))`

∴ h₂ = `(0.55xx2.2)/6.6`

= `1.21/6.6`

∴ h₂ = 0.183 m
i.e., h₂ ≈ 0.2 m

Hence, the size of the image of the minibus is nearly a square of edge 0.2 m.