Question

When you look at yourself in a convex mirror, you appear to be ¼ your actual size. If you are standing 1.0 m in front of the mirror, what is the mirror’s focal length and radius of curvature. (Be sure to first sketch the situation).

Answer 1

The focal length is
`f = -0.2 \ m`

The radius of curvature is
`R = -0.4 \ m`

Step-by-step explanation:

From the question we are told that

The magnification of the mirror is
`m = (1)/(2)`

The distance of the person from the mirror(the object distance ) is
`u = - 1.0 \ m`

The negative sign shows that it is been placed in front of the mirror

Generally the magnification of the mirror is mathematically represented as

`m = (v)/(u)`

=>
`(1)/(4) = (v)/(-u)`

=>
`v = (- 1)/(4)`

Generally from the lens equation we have that

`(1)/(f) = (1)/(u) + (1)/(v)`

=>
`(1)/(f) = (1)/(-1 ) + (1)/(-(1)/(4) )`

=>
`f = -0.2 \ m`

Generally the radius of curvature is mathematically represented as

`R = 2 * f`

=>
`R = 2 * - 0.2`

=>
`R = -0.4 \ m`