How Does the Presence of Thick Glass Affect Image Formation in a Concave Mirror?

[Volcano]

A glass is located in front of concave mirror as shown in figure. The gap between mirror and glass is neglected. In this conditions, where is the final image of matter?

http://i26.tinypic.com/2a6w6es.jpg

The answer of above problem is not match with mine. I need help.

I draw the beams as below, since the gap between mirror and the glass neglected, i think the figure is approximately the same as above.

http://i31.tinypic.com/2yplsif.jpg

If the roads of beam right then the final image of matter is between focus and center of curvature. But the book say it is far from center of curvature. What do you think?

 

[Volcano]

any help? Any physicist :)

 

[alphysicist]

Hi Volcano,

I don't think you can treat the concave mirror as a plane mirror. When they say the space can be neglected, that should mean that you can ignore the distance between the back of the glass and the mirror when you calculate distances for your equations.

By the way, you wrote that the book said it is far from center of curvature; what exactly did the book say? Did you mean that it's on the far side (on the side opposite the mirror), or that it is a large distance from the center of curvature?

 

[mgb_phys]

No you can't assume it is a plane mirror.
The trick is that light passing through a parallel sided block is simply moved sideways while still traveling in the same direction, the shift depends on the angle, the thickness of the block and the refractive index.

Light going parallel into the block isn't changed.

 

[Volcano]

Thank you,

I don't think you can treat the concave mirror as a plane mirror.

No, I didn't treat it as plane mirror. It is already spherical but removed the gap. Furthermore all beams drawed for a spherical mirror.

Honestly, I didn't like the second figure which i sketch. The better would be only fill the gap with the same block beside adapting the mirror to block :)

mgb_phys, ok, I agree. The image position vary with the thickness of the block and the refractive index. And if there is a gap between mirror and block then it would be shift and it would be change with the angle. But already the body would give an image on primary axis is it?

Let's correct the figure and say the gap is also filled by the block thus, mirror and block sticked each other. Where would be the image of the body? I suppose between F-C.