Radius of Curvature of Convex Mirror: -17.39 cm

In summary, a real object is placed at the zero end of a meterstick and a large concave mirror forms an image of the object at the 82.4 cm position. A small convex mirror placed at the 20 cm position forms a final image at the 6.3 cm point. Using the equation 1/do + 1/di = 1/f, the focal length of the convex mirror is calculated to be 34.78 cm and the radius of curvature is 69.56 cm.
  • #1
Niendel
2
0
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!
 
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  • #2
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.
 
  • #3


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.
 

Related to Radius of Curvature of Convex Mirror: -17.39 cm

What is the definition of the radius of curvature of a convex mirror?

The radius of curvature of a convex mirror is the distance from the center of the mirror to the center of its curvature. It is also referred to as the focal length of the mirror.

How is the radius of curvature of a convex mirror calculated?

The radius of curvature of a convex mirror can be calculated using the formula R = 2f, where R is the radius of curvature and f is the focal length of the mirror.

What does a negative radius of curvature indicate for a convex mirror?

A negative radius of curvature for a convex mirror indicates that the mirror is a diverging mirror, meaning that it spreads out light rays instead of converging them. In this case, the center of curvature is located behind the mirror.

What is the significance of a value of -17.39 cm for the radius of curvature of a convex mirror?

A value of -17.39 cm for the radius of curvature of a convex mirror indicates that the mirror has a focal length of -8.69 cm, which means that it is a small, highly curved mirror with a strong diverging effect on light rays.

How does the radius of curvature affect the image produced by a convex mirror?

The radius of curvature directly affects the size and location of the image produced by a convex mirror. The smaller the radius of curvature, the smaller and closer the image will be to the mirror. Additionally, a smaller radius of curvature will result in a wider field of view for the mirror.

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