Focal length of a convex mirror

Click For Summary
SUMMARY

The focal length of a convex mirror can be determined using the object distance and the image distance derived from the problem statement. An object placed 12.0 cm in front of the convex mirror results in a virtual image located 7.0 cm behind the mirror. The flat mirror, positioned 5.0 cm farther away, produces an image at 12.0 cm. Applying the mirror formula, 1/do + 1/di = 1/f, yields a focal length of -0.12 m for the convex mirror, confirming that the image is virtual.

PREREQUISITES
  • Understanding of mirror equations, specifically 1/do + 1/di = 1/f
  • Knowledge of convex mirror properties and image formation
  • Familiarity with the concept of virtual and real images
  • Basic skills in unit conversion (cm to m)
NEXT STEPS
  • Study the derivation of the mirror formula and its applications
  • Learn about the characteristics of virtual images produced by convex mirrors
  • Explore ray diagrams for convex mirrors to visualize image formation
  • Investigate the relationship between object distance, image distance, and focal length in concave mirrors for comparison
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding the principles of mirror image formation and focal lengths.

aChordate
Messages
76
Reaction score
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
?
 
Physics news on Phys.org
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
 
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?
 
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
 
di=12cm for the flat mirror
di=7cm for the convex mirror?
 
Using the above di, I got f=0.12m.
 
The image is behind the mirror.
 
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
 
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.
 

Similar threads

Replies
19
Views
960
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
3
Views
5K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K