Answer to Question #123695 in Physics for aiben

Question

magnification produced by a concave mirror is -1 .what does it mean ? a mirror produces a magnification of +3/5 when an object is placed at a distence of 20cm from the mirror .find postion of image at focal length of mirror

Answer 1

The phrase "magnification produced by a concave mirror is -1" means that the size of the image is equal to the size of the object (because magnification is image size divided by object size or image distance divided by object distance). The sign "-" means that the image is inverted.

This will help us to solve the next part.

Using magnification, find image distance:

$$M=-\frac{i}{o}=\frac{3}{5},\\\space\\ -\frac{i}{20}=\frac{3}{5},\\\space\\ i=-12\text{ cm}.$$

Using the concave mirror formula, find the focal length:

$$\frac{1}{f}=\frac{1}{i}+\frac{1}{o},\\\space\\ \frac{1}{f}=\frac{1}{-12}+\frac{1}{20},\\\space\\ f=-30\text{ cm}.$$