Answer :
Answer:
The focal length is 16.86 cm and the distance of the man if he wants to form an upright image of his chin that is twice the chin's actual size is 8.43 cm.
Explanation:
Given that,
Object distance u=1.54 m =154 cm
Image distance v = 15.2 cm
Magnification = 2
We need to calculate the focal length
Using formula of mirror
[tex]\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}[/tex]
Put the value into the formula
[tex]\dfrac{1}{f}=\dfrac{1}{15.2}+\dfrac{1}{-154}[/tex]
[tex]\dfrac{1}{f}=\dfrac{347}{5852}[/tex]
[tex]f=16.86\ cm[/tex]
We need to calculate the focal length
Using formula of magnification
[tex]m= \dfrac{-v}{u}[/tex]
Put the value into the formula
[tex]2=\dfrac{v}{u}[/tex]
[tex]v = -2u[/tex]
Using formula of for focal length
[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]
[tex]\dfrac{1}{16.86}=\dfrac{1}{u}-\dfrac{1}{2u}[/tex]
[tex]\dfrac{1}{16.86}=\dfrac{1}{2u}[/tex]
[tex]2u=16.86[/tex]
[tex]u=\dfrac{16.86}{2}[/tex]
[tex]u=8.43\ cm[/tex]
Hence, The focal length is 16.86 cm and the distance of the man if he wants to form an upright image of his chin that is twice the chin's actual size is 8.43 cm.