Question

-An object whose height is 5.8 cm is at a distance of 9.5 cm from a spherical concave mirror. Its image is real and has a height of 9.2 cm. Calculate the radius of curvature of the mirror.

I got 0.1165 m for my answer.

-How far from the mirror is it necessary to place the above object in order to have a virtual image with a height of 9.2 cm?

I know that I have two unknowns to solve for, but how do I go about solving them?

Answer 1

Use the desired image height and the object height to get the magnification ratio: it is 9.2/5.8 = 1.586

Since you want the image to be virtual, the Do value must be negative, and such that |Di/Do| = 1.58 (the magnification)

Therefore Di = -1.58 Do

Use that together with the focusing equation

1/Do + 1/Di = 2/R

to solve for Do. You already know R.

Answer 2

I get as far as 1/Do + 1/-1.58 = 17.167, but I'm not sure what my next step is.

Answer 3

Wrong equation

1/Do + 1/-1.58Do = 17.167

Solve for Do