A spherical mirror is to be used to form an image 270 times

A spherical mirror is to be used to form an image 2.70 times the size of an object on a screen located 5.40 m from the object. (a) Is the mirror required concave or convex?

1

concave convex   

(b) What is the required radius of curvature of the mirror?

Your response differs from the correct answer by more than 10%. Double check your calculations. m

(c) Where should the mirror be positioned relative to the object?

Solution

(1). Concave mirror

(2).Magnification m = v/u = 2.7

             v = 2.7 u        --------( 1)

Distance of the object and screen v+u = 5.4 m

               2.7 u + u = 5.4 m

                   3.7 u = 5.4 m

                        u = 5.4m /3.7

                          = 1.459 m

From equation(1) , v = 2.7 u = 2.7 x 1.459 = 3.94 m

From the relation (1/u ) +(1/v) = (1/f)

                ( 1/1.459) +(1/3.94) = (1/f)

                                  ( 1/f) = 0.9391

                                       f = 1.064 m

the required radius of curvature of the mirror R = 2f

                                                                   = 2(1.064 m)

                                                                   = 2.129 m

(c).The object is in between focus and center of curvature.

and distance u = 1.459 m