Question

I wrote an email to the manufacture of my bike's rear view mirror that the following warning should also be written on it: 'objects are faster than they appear' on my rear view mirror. Will this warning always be true?

• A. No
• B. Yes
• C. Data insuffcient to comment

Answer 1

The correct option is B Yes

The driver will be in the mirror frame of reference (velocity of the driver =velocity of the mirror) . So, we have the formula for the velocity of the image in terms of velocity of the object from the mirror's frame of reference.
As we discussed the mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ is always true from the mirror frame of referance, hence,
$\overrightarrow{vi{,}_m}=\overrightarrow{c{v}_{o,m}}(Wherec=\frac{f^2}{(f-u{)}^2.}).$
Now, the value of c will give us the comparison between the speed of the image and the speed of the object.
We have, $c=\frac{f^2}{(f-u{)}^2}$ By taking proper sign convention,
As we have a convex mirror here, f will be +ve and u will be −ve.
In this case (taking u and f to be of opposite signs), f − u > f (always)
So, c < 1 always.
Hence, the magnitude of the velocity of the image w.r.t mirror will always be less than the
magnitude of the velocity of the object w.r.t mirror.
Hence, there is no technical harm in saying that :
Objects in the mirror are faster than they appear.