Trying to find the image of an object reflected through a lens and

[exparrot]

then through a plane mirror (I could put that all down in the title!)

Homework Statement

A bright object 1 cm tall is located at x = -6 cm. There is a thin lens atx = 0 with focal length f = 4 cm, and a plane mirror located at x = 7 cm. Light from the object passes through the lens, reflects off the mirror, and then passes through the lens again to form an image.

(a) Where is the final image located? Is it real or virtual?

(b) What is the height of the final image?

Homework Equations

I drew a ray diagram for when the object is reflected through the lens. Disregarding the plane mirror, I found image is inverted at about 12 cm. I know that that the rays should reflect off the plane mirror (following the law of reflection), but when I draw my rays, the focal ray, which is perpendicular to the plane mirror, is reflected in the same direction it hit the mirror. However my parallel and central rays hit the bottom of the lens and then I'm not quite sure what the rays should look like after that.

The Attempt at a Solution

Drew my ray diagram for when the object is reflected through the lens. Not quite sure how to work around the plane mirror...

 

[rl.bhat]

Mirror is placed at 7 am from the lens. So the distance of the virtual object behind the mirror is 5 cm. In the mirror object distance equal to the image distance. If the object is real, image is virtual. And If the object is virtual, the image is real. Hence the image is real at 2 cm from the lens. Now find the final image.

 

[ashishsinghal]

Since most of your work is a ray diagram it would be good if you post it here...

 

[exparrot]

Mirror is placed at 7 am from the lens. So the distance of the virtual object behind the mirror is 5 cm. In the mirror object distance equal to the image distance. If the object is real, image is virtual. And If the object is virtual, the image is real. Hence the image is real at 2 cm from the lens. Now find the final image.

Okay, that makes sense. Thanks for your help!

 

[rwisz]

I would suggest using the thin lens formula and the mirror equation to solve for the image location and height. The thin lens formula is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. The mirror equation is 1/do + 1/di = 1/f, where do is the object distance and di is the image distance. By combining these equations, you can solve for the final image location and determine whether it is real or virtual.

As for the ray diagram, you can use the law of reflection to determine the direction of the reflected rays after they hit the plane mirror. The focal ray will still be perpendicular to the mirror, but the parallel and central rays will be reflected at the same angle as they hit the mirror. You can then use these reflected rays to construct the final image location and height on the ray diagram.

Overall, it is important to use a combination of equations and diagrams to accurately determine the final image location and height when light passes through a lens and reflects off a plane mirror.