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An object is placed to the left of a convex mirror, such that the object-to-image distance is 140 cm.

Find the focal length of the mirror, if the image is 35 cm from the mirror.

Please explain step by step as I do not know how to do this properly. Thank you!

Answer :

Answer:

The focal length of the mirror is 52.5 cm.

Explanation:

Given that,

Object to Image distance d = 140 cm

Image distance v= 35 cm

We need to calculate the object distance

[tex]u = d-v[/tex]

[tex]u = 140-35=105\ cm[/tex]

We need to calculate the focal length

Using formula of mirror

[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]

Put the value into the formula

[tex]\dfrac{1}{f}=\dfrac{1}{-105}+\dfrac{1}{35}[/tex]

[tex]\dfrac{1}{f}=\dfrac{2}{105}[/tex]

[tex]f=52.5\ cm[/tex]

Hence, The focal length of the mirror is 52.5 cm.

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