Question

A 3.92 cm tall object is placed in 31.3 cm in front of a convex mirror. The focal

Answer 1

Answer:

0.29

Explanation:

We can find the position of the image by using the mirror equation:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$

where:

f is the focal length of the mirror

p is the distance of the object from the mirror

q is the distance of the image from the mirror

For the mirror in this problem:

f = -12.7 cm (the focal length of a convex mirror is negative)

p = 31.3 cm (distance of the object)

Solving for q, we find the position of the image:

$\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-12.7}-\frac{1}{31.3}=-0.111 cm^{-1}\\q=\frac{1}{-0.111}=-9.1 cm$

And so, the magnification of the image is:

$M=-\frac{q}{p}$

And substituting,

$M=-\frac{-9.1}{31.3}=0.29$

Which means that the image is upright (positive sign) and diminished (M is smaller than 1).