Focal length of a convex mirror

[aChordate]

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/d_o+1/d_i=1/f

The Attempt at a Solution

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

12+5cm=17cm=0.17m

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

 

[ehild]

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/d_o+1/d_i=1/f

The Attempt at a Solution

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

12+5cm=17cm=0.17m

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

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


ehild

 

[aChordate]

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


ehild

They would be equidistant to the mirror?

 

[ehild]

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

 

[aChordate]

di=12cm for the flat mirror
di=7cm for the convex mirror?

 

[aChordate]

Using the above di, I got f=0.12m.

 

[Basic_Physics]

The image is behind the mirror.

 

[ehild]

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

 

[PeterO]

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/d_o+1/d_i=1/f

The Attempt at a Solution

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

12+5cm=17cm=0.17m

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

Have you solved the problem? A quick ray Trace will do it for you.

 

[Basic_Physics]

The problem statement tells us that the image is behind the mirror.