Question

An upright object is placed in front of a concave mirror. The radius of curvature of mirror is 40 cm.
(a) Where should the object be placed in order to obtain an image that is twice as large as the object?
(b) Is the image upright or inverted?

SHOW ALL STEPS & DIAGRAM

Answer 1

This problem uses the mirror equation , and the magnification equation where s the object distance to the mirror, is the image distance, R is the radius of curvature of the mirror, is the image height and y is the object height.

(a)

Step 1) First use the magnification equation. We're told that the image height is twice that of the object height, so . Plug this into the magnification equation.

Step 2) Now plug the above expression found for into the mirror equation, along with the radius of curvature .

The object should be placed 10 cm in front of the mirror.

(b)

Step 3) To determine if the image is upright or inverted, look at the magnification equation again. Plug in .

Since the magnification is positive, the image is upright. Be careful to note though that this is how we designed it, by assuming the image height was twice that of object height. We could have assumed it had a magnification of -2, meaning the image was still twice the height of the object, but upsidedown (inverted). This would've yielded a different value for the object distance.