What is the correct formula for calculating focal length in convex mirrors?

In summary, when studying for a test covering mirrors and lenses, the focal length for a concave or convex mirror is typically equal to half the radius of curvature. However, a question in the book used a different value for f, causing confusion. Upon further examination, it was determined that it was a typo and the correct equation is 1/f = 2/r. This was used in the problem where the right hand side was replaced with -2/20yd.
  • #1
kankerfist
35
0
I'm studying for a test that is going to cover mirrors and lenses. I was under the impression that the focal length for any concave or convex mirror was half the radius of curvature:
f=r/2

but one of the questions in my book involving a convex mirror uses a different value for f, according to the solutions manuel. It says that:
f=2/r

of all the questions I've encountered while studying for this test, f has always been r/2. can someone help explain why f can be 2/r?
 
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  • #2
That does seem like a typo. As r gets bigger, f will grow. Can you state the exact problem from the text?
 
  • #3
So was that a typo? Test tomorrow...
 
  • #4
kankerfist said:
So was that a typo? Test tomorrow...
Yes it was a typo. They meant to say 1/f = 2/r and that is the way they used it in the problem. The right hand side of the next to last line replaced the 1/f with -2/20yd
 

What is mirror reflection?

Mirror reflection is the phenomenon where light bounces off a smooth surface, such as a mirror, and creates a virtual image of the objects in front of it. This creates the illusion of a reversed image, giving the appearance of a reflection.

How does mirror reflection work?

Mirror reflection works through the process of reflection, where light bounces off a smooth surface at the same angle at which it hits the surface. This creates a virtual image of the objects in front of the mirror, giving the illusion of a reflection.

Why do mirrors reflect images?

Mirrors reflect images because they have a smooth and highly reflective surface. When light hits the surface, it bounces off at the same angle, creating a virtual image of the objects in front of it.

What is the difference between a plane mirror and a curved mirror?

A plane mirror has a flat and smooth surface, while a curved mirror has a curved surface. This results in different types of reflections. A plane mirror creates a virtual image that is the same size as the object, while a curved mirror can create magnified or diminished images depending on the curvature.

How is mirror reflection used in everyday life?

Mirror reflection is used in many everyday objects, such as mirrors, windows, and even in eyesight. It is also used in various technologies, such as telescopes, cameras, and lasers. Additionally, mirror reflection is used in art and design to create symmetrical and visually appealing compositions.

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