Radius of Curvature of Convex Mirror: -17.39 cm

[Niendel]

A real object is placed at the zero end of a meterstick. A large concave mirror at the 100 cm end of the meterstuck forms an image of the object at the 82.4 cm position. A small convex mirror placed at the 20 cm pisition form a final image at the 6.3 cm point. What is the radius of curvature of the convex mirror? Answer in unites of cm.

So i know that since i have 2 mirrors the image for the 1st image will be the object for the 2nd mirror.

Therefore Di= -13.6 cm
Do=62.4 cm

since 1/do + 1/di = 1/f
f = -17.39
therefore Since r=2F
r should be -17.39 cm according to my calculations but I am doing something wrong cause this is not the answer!

 

[Nate810]

Can someone please explain to me what I am doing wrong here? You are forgetting that the focal length of a convex mirror is positive. So, instead of 1/do + 1/di = 1/f, you should use 1/do - 1/di = 1/f. This means that f = 34.78 cm and r = 69.56 cm.

 

[kyle8921]

Thank you for providing the information about the radius of curvature of the convex mirror. Based on the given information, it seems that there may be some error in your calculations. The correct radius of curvature for the convex mirror can be determined by using the formula r = 2f, where f is the focal length of the convex mirror. In this case, the focal length can be calculated by using the equation 1/do + 1/di = 1/f, where do is the object distance and di is the image distance. By substituting the values given in the problem, we get f = -12.6 cm. Therefore, the radius of curvature of the convex mirror is 2*(-12.6) = -25.2 cm. I hope this helps clarify your calculations.