Focal length of a convex mirror

In summary: In order to solve the problem, we need to find the focal length of the convex mirror. We can do this by using the equation 1/f=1/R. So, in this case, the focal length of the convex mirror is 0.17 meters.
  • #1
aChordate
76
0

Homework Statement



An object is 12.0 cm in front of a convex mirror. When the convex mirror is replaced
with a flat mirror, the image distance is 5.0 cm farther away from the mirror. What is the
focal length of the convex mirror?

Homework Equations



f=-1/2R

1/do+1/di=1/f

The Attempt at a Solution



(1/0.12m)+1/di=1/f
?

12+5cm=17cm=0.17m

(1/0.17m)+1/di=1/f
?
 
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  • #2
aChordate said:

Homework Statement



An object is 12.0 cm in front of a convex mirror. When the convex mirror is replaced
with a flat mirror, the image distance is 5.0 cm farther away from the mirror. What is the
focal length of the convex mirror?

Homework Equations



f=-1/2R

1/do+1/di=1/f

The Attempt at a Solution



(1/0.12m)+1/di=1/f
?

12+5cm=17cm=0.17m

(1/0.17m)+1/di=1/f
?

How is the image distance related to the object distance in case of a flat mirror?


ehild
 
  • #3
ehild said:
How is the image distance related to the object distance in case of a flat mirror?


ehild

They would be equidistant to the mirror?
 
  • #4
Yes. So the mirror image in case of flat mirror is farther away by 5 cm than the image produced by the convex mirror. If the object distance is 12 cm and the image distance is shorter by 5 cm, what can be di?

ehild
 
  • #5
di=12cm for the flat mirror
di=7cm for the convex mirror?
 
  • #6
Using the above di, I got f=0.12m.
 
  • #7
The image is behind the mirror.
 
  • #8
aChordate said:
di=12cm for the flat mirror
di=7cm for the convex mirror?
The image is at 7 cm distance from the mirror, but the mirror is convex, is the image virtual or real?
What is the sign of di ? ehild
 
  • #9
aChordate said:

Homework Statement



An object is 12.0 cm in front of a convex mirror. When the convex mirror is replaced
with a flat mirror, the image distance is 5.0 cm farther away from the mirror. What is the
focal length of the convex mirror?

Homework Equations



f=-1/2R

1/do+1/di=1/f

The Attempt at a Solution



(1/0.12m)+1/di=1/f
?

12+5cm=17cm=0.17m

(1/0.17m)+1/di=1/f
?

Have you solved the problem? A quick ray Trace will do it for you.
 
  • #10
The problem statement tells us that the image is behind the mirror.
 

What is the focal length of a convex mirror?

The focal length of a convex mirror is the distance from the mirror's surface to the point where all reflected light rays converge. It is denoted by the letter "f" and is measured in meters.

How is the focal length of a convex mirror determined?

The focal length of a convex mirror can be determined by using the formula f = R/2, where R is the radius of curvature of the mirror. The radius of curvature is the distance from the center of the mirror to its curved surface.

What is the relationship between the focal length and the size of the image in a convex mirror?

The focal length of a convex mirror is inversely proportional to the size of the image formed. This means that as the focal length increases, the size of the image decreases, and vice versa.

Can the focal length of a convex mirror be negative?

Yes, the focal length of a convex mirror can be negative. This occurs when the object is placed between the focal point and the mirror's surface. In this case, the image formed is virtual and upright.

How does the focal length of a convex mirror affect the magnification of the image?

The focal length of a convex mirror has a direct impact on the magnification of the image formed. As the focal length decreases, the magnification increases, resulting in a larger and closer image. Conversely, as the focal length increases, the magnification decreases, resulting in a smaller and farther image.

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