Answer to Question #156726 in Optics for Alessia

Question

A concave mirror has a focus of 75cm. An object is placed 60cm in front of the mirror. Describe the image characteristics of this object

Answer 1

Let's use the mirror equation and find the image distance:

$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$ $d_i=(\dfrac{1}{f}-\dfrac{1}{d_o})^{-1},$ $d_i=(\dfrac{1}{75\ cm}-\dfrac{1}{60\ cm})^{-1}=-300\ cm.$

The sign minus means the the image is virtual and located behind the mirror.

Let's find the magnification of the image from the magnification eqquation:

$M=\dfrac{-d_i}{d_o}=\dfrac{-(-300\ cm)}{60\ cm}=5.$

The sign positive means that the image is upright and larger than the object.

Answer:

The image is virtual and located behind the mirror, upright and larger than the object.