Optics : How many images can be seen in inclined mirrors?

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]
I tried to draw a rough figure depicting the situation.

Here M is the mosquito and I₁, I₂, I₃ are its images .

Mosquito can clearly see it's image I₁ .Now whether it can see I₂and I₃ is something I am not too sure .

For that I first considered image I₂ .M can only see I₂ if ray PM is such that it has been originated at M and undergone two reflections at mirrors R1 and R2.Since the mosquito is very close to R1 and mirrors are inclined at an obtuse angle, we cannot draw such multiple reflected rays .

Similar reasoning lies for image I₃ . So I think option B) is correct.

Is my reasoning correct ?

 

[Doc Al]

I think your reasoning is OK, but there's an easier way to consider images with plane mirrors. Think of each mirror as a window into a parallel world where the images lie. Those images are exactly behind those mirrors, along a line normal to the surface. So, assuming I₂ is the image of M in mirror R2, then ask: Can M look through that "window" and see I₂? No.

Similarly, if I₃ is the reflection of I₁ in mirror R2, then can M see it by looking through the "window" of mirror R2? Again, no.

 

[Jahnavi]

Can M look through that "window" and see I₂? No.

Why ? Can M see only along a normal ? Is extension of mirror not considered part of window ?

Sorry . I am not understanding this window concept .

Can you explain how does mosquito see the images through the window?

 

[CWatters]

If the mosquito is looking at images of itself then I think your drawing is wrong. The light must originate from and return to the mosquito.

 

[Jahnavi]

If the mosquito is looking at images of itself then I think your drawing is wrong.

These three are images formed by the mirrors , not images which can be seen by M .

The light must originate from and return to the mosquito.

This is what I did to reason out why only one image can be seen .

 

[SammyS]

Why ? Can M see only along a normal ?

For the mosquito to see an image of itself, a ray originating at the mosquito must be reflected back to the mosquito. That's along a normal. Right?

 

[Jahnavi]

For the mosquito to see an image of itself, a ray originating at the mosquito must be reflected back to the mosquito. That's along a normal. Right?

Normal to what ?

Please use the sketch I have made to specify .

 

[SammyS]

Normal to what ?

Please use the sketch I have made to specify .

I was answering your question:

Can M see only along a normal ?

I was explaining why the image the mosquito sees of itself in a (single) plane mirror is along the normal from the mosquito through the mirror.

 

[Jahnavi]

To be more specific , let us work with notations used in the sketch .

I₃ is image of M in R₂ .I₂ is image of I₁ in R₂ .

Is that ok with you ?

 

[SammyS]

To be more specific , let us work with notations used in the sketch .

I₃ is image of M in R₂ .I₂ is image of I₁ in R₂ .

Is that ok with you ?

That is helpful.

Also helpful is to use the ":Reply" feature to make clear which post you are replying to.The image, I₃, of mosquito, M, in R₂ should be along the normal from M through R₂, or R₂ extended. For your drawing, this normal passes very near to O. For M closer to R₁ and/or farther from R₂, the mosquito will definitely not be able to view this image. I₃ is misplaced.

I₂ looks to be reasonably well placed, and is definitely not view-able at M.

 

[Jahnavi]

I₂ looks to be reasonably well placed, and is definitely not view-able at M.

Could you explain your reasoning ?

 

[SammyS]

Could you explain your reasoning ?

You show a ray going to M from the direction of I₂, but where does that come from? Not from the Mosquito. While the placement of I₂ looks fine, the dashed line to I₂ and the arrowhead on the ray pointing to M are both misleading.

The ray would start at M, be reflected twice and exit out the top of the figure. An observer along the ray after the two reflections would see the image at I₂. A dashed line from I₂ to the point of intersection of the ray and R₂ would be correct.

 

[Jahnavi]

You show a ray going to M from the direction of I₂, but where does that come from? Not from the Mosquito. While the placement of I₂ looks fine, the dashed line to I₂ and the arrowhead on the ray pointing to M are both misleading.

The ray would start at M, be reflected twice and exit out the top of the figure. An observer along the ray after the two reflections would see the image at I₂. A dashed line from I₂ to the point of intersection of the ray and R₂ would be correct.

Well , this same reasoning I had stated/intended in the OP

I thought , may be you had @Doc Al 's reasoning using the window in your mind .

May be @Doc Al can explain his post .

 

[Jahnavi]

I think your reasoning is OK, but there's an easier way to consider images with plane mirrors. Think of each mirror as a window into a parallel world where the images lie. Those images are exactly behind those mirrors, along a line normal to the surface. So, assuming I₂ is the image of M in mirror R2, then ask: Can M look through that "window" and see I₂? No.

Similarly, if I₃ is the reflection of I₁ in mirror R2, then can M see it by looking through the "window" of mirror R2? Again, no.

When is M able to see I2 and I3 ?

Since I2 and I3 are images formed in mirror R2 , if I draw a line joining M and I2 , that line should intersect R2( not the extended part ) .Then M can see image I2 .

But if that line doesn't intersect the real visible part of R2 and instead intersects the extended part of mirror R2 , then M cannot see image I2

Is that what you intended in your post ?

Another thing I need to clarify is that , the concerned window should be of that mirror only whose image M wants to see .For example , since I2and I3 are images from R2 , the concerned window should be of R2 only , not R1 .

Not sure if it makes sense ?

 

[CWatters]

Draw a line from the point where the mirrors meet and normal to R2. Can the mosquito be above this line and still be close to R1? Badly worded question?

 

[Doc Al]

Why ? Can M see only along a normal ? Is extension of mirror not considered part of window ?

Sorry . I am not understanding this window concept .

Can you explain how does mosquito see the images through the window?

Let's go over an example that might help.

Imagine a mirror in the y = 0 plane that extends from x = 0 to x = 10 meters. You stand at point (11, 1). So you are off to the side of the mirror, facing a blank wall. Where is your image in the mirror? At point (11, -1). Can you see it? No! Think of the mirror as a window. Looking through that window, can you see your image? No -- it's behind a wall!

Now consider a friend standing at point (1, 1). His image is at point (1, -1). Can he see his image? Sure, he's right in front of that mirror "window". Can he see your image? Sure. Can you see his image in the mirror? Sure. (Of course it's not really a window, it's a mirror. So you are really only seeing reflections. But it works out as if it were a window.)

If you imagine an image world behind the plane of the mirror, then you can easily determine whether an observer can see any particular image by treating the mirror as a 'window' into that image world. (Any extension of the plane of the mirror is a wall, not a window.)

Let me know if that's any clearer.

 

[Jahnavi]

(Any extension of the plane of the mirror is a wall, not a window.)

Ok.

I think my earlier post goes in line with your reasoning .

Please see post 14 and let me know whether you find it reasonable .

 

[Doc Al]

When is M able to see I2 and I3 ?

Since I2 and I3 are images formed in mirror R2 , if I draw a line joining M and I2 , that line should intersect R2( not the extended part ) .Then M can see image I2 .

But if that line doesn't intersect the real visible part of R2 and instead intersects the extended part of mirror R2 , then M cannot see image I2

Is that what you intended in your post ?

Yes.

Another thing I need to clarify is that , the concerned window should be of that mirror only whose image M wants to see .For example , since I2and I3 are images from R2 , the concerned window should be of R2 only , not R1 .

Not sure if it makes sense ?

Perfect. You've got it now.

(You should play around with some examples of your own making to convince yourself that it always works.)

 

[Jahnavi]

Thanks so much . You have been really nice .