Question

A spherical, concave shaving mirror has a radius of curvature of 0.983 m. What is the magnification of a person's face when it is 0.155 m from the vertex of the mirror (answer sign and magnitude)

Answer 1

The magnification is 1.5.

Step-by-step explanation:

radius of curvature, R = - 0.983 m

distance of object, u = - 0.155 m

Let the distance of image is v.

focal length, f = R/2 = - 0.492 m

Use the mirror equation

`(1)/(f)=(1)/(v)+\frac {1}{u}\\\\(-1)/(0.492)=(1)/(v)-(1)/(0.155)\\\\(1)/(v)=(1)/(0.155)-(1)/(0.492)\\\\(1)/(v)=(0.492-0.155)/(0.155* 0.492)\\\\(1)/(v)=(0.337)/(0.07626)\\ \\v = 0.226 m`

The magnification is given by

m = - v/u

m = 0.226/0.155

m = 1.5

Answer 2

Magnification = 1

Step-by-step explanation:

given data

radius of curvature r = - 0.983 m

image distance u = - 0.155

solution

we get here first focal length that is

Focal length, f = R/2 ...................1

f = -0.4915 m

we use here formula that is

`(1)/(v) + (1)/(u) + (1)/(f)` .................2

put here value and we get

`(1)/(v) = (1)/(0.155) - (1)/(4915)`

v = 0.155 m

so

Magnification will be here as

m =
`- (v)/(u)`

m =
`(0.155)/(0.155)`

m = 1