A convex mirror on the passenger side of a car produces an image of a vehicle that is 20.3 m from the mirror. If the image is located 50.4 cm behind the mirror, what is the radius of curvature of the mirror?

Explanation:

A representative diagram with sign convention has been shown below. Assuming that mirror is thin having the focal length and the radius of curvature , so that .

Here, the object side is negative and the image side is positive as give that image is behind the mirror.

Let and be the object and image distance respectively, so and .

Now, from the mirror formula

Putting the given values in the above formula, we have

Now, from the equation

Hence, the radius of curvature of the mirror is .