Question

Consider a makeup mirror that produces a magnification of 1.5 when a person's face is 11.5 cm away what is the focal length of the makeup mirror in meters?

Answer 1

Answer: The focal length of makeup mirror is 0.3448 m.

Explanation:

We are given:

m = 1.5

u = -11.5 cm

To calculate the image distance, we the equation for mirror:

$m=-\frac{v}{u}$

Putting values in above equation, we get:

$1.5=-(\frac{v}{-11.5})\\\\v=17.25cm$

To calculate the focal length of mirror, we use the mirror formula, which is:

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Putting values in above equation, we get:

$\frac{1}{f}=\frac{1}{17.25}+\frac{1}{-11.5}\\\\f=-34.48cm$

Negative sign represents the position of focal length.

Converting the focal length into meters, we use the conversion factor:

1 m = 100 cm

So, 34.48 cm = 0.3448 m

Hence, the focal length of makeup mirror is 0.3448 m.