Question

You're asked to design a concave mirror that will produce a virtual image, enlarged 1.7 times, of an object 17 cm from the mirror.

Part A

What do you specify for the mirror's curvature radius?

Express your answer with the appropriate units.

R =

Show me every single step please

Answer 1

We have a mirror formula as

                        --------------------- formula 1

and                             -------------------- formual 2

where f = focal length of mirror

            v = image distance

            u = object distance

We have m = 1.7

                 u = -17 cm

since

1.7 = -v /(-17)

1.7 * 17 = v

28.9 cm = v

Now as we have both u = -17 cm and v = 28.9 cm we can find the focal length by formula 1

         

1/f = 1/(-17) + 1/28.9

      =

so f = -28.9/0.7

        = - 41.28 cm

Since the calculated focal length of concave mirror is 41 .28 cm then its radius of curvature will be

41.28 *2 = 82.56 cm