A convex surveillance mirror in a convenience store has a focal length of 10.40 m A customer, who is 1.7 all, is standing 4.5 m ir front of the mirror a. Calculate the image distance. b. Calculate the image height

Question

Answer 1

To solve this problem, we will use the mirror equation and magnification formula. The mirror equation is given by:

where:-

is the focal length of the mirror,-

is the object distance (distance from the object to the mirror),-

is the image distance (distance from the image to the mirror).The magnification

is given by:

where:-

is the image height,-

is the object height.Given:- Focal length

(negative for convex mirrors),- Object distance

,- Object height

.### a. Calculate the image distance (

)Using the mirror equation:

First, calculate

:

Now substitute into the equation:

Subtract 0.2222 from both sides:

Now take the reciprocal to find

:

The negative sign indicates that the image is virtual and located on the same side of the mirror as the object.### b. Calculate the image height (

)Using the magnification formula:

Substitute the known values:

Now calculate the image height:

Thus, the image height is approximately

.

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