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:
[tex]m=-\frac{v}{u}[/tex]
Putting values in above equation, we get:
[tex]1.5=-(\frac{v}{-11.5})\\\\v=17.25cm[/tex]
To calculate the focal length of mirror, we use the mirror formula, which is:
[tex]\frac{1}{f}=\frac{1}{v}+\frac{1}{u}[/tex]
Putting values in above equation, we get:
[tex]\frac{1}{f}=\frac{1}{17.25}+\frac{1}{-11.5}\\\\f=-34.48cm[/tex]
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.
