Question

What is the radius of curvature of a concave mirror that magnifies an object placed 30.0cm from the mirror by a factor of+3.0

Answer 1

as we know, focus of lens = radius of curvature/2

Answer 2

Answer:

Radius of curvature of a concave mirror is 45 cm .

Explanation:

A concave mirror is a sort of spherical mirror in which the reflecting surface is the sphere's inner curved surface.

Below is the mirror equation for a concave mirror.  

          $\frac{1}{u} + \frac{1}{v} =\frac{2}{R}$    

        u = distance  of object from radius of curvature  

        v= distance of image formed  from radius of curvature  

        R= Radius of curvature  

Now magnification factor is given as

 M = -v/u

Given :                  M= 3    u = 30 cm

so , calculating v  

  M = -v /30  

 v = - 3× 30  

v = - 90 cm

using mirror equation  

 $\frac{1}{30} +\frac{1}{-90}= \frac{2}{R}$

   $\frac{1}{30} - \frac{1}{90} =\frac{2}{R}$  

  $\frac{3-1 }{90} = \frac{2}{R}$  

  $R = 90 cm$

Hence radius of curvature is 90 cm .