What is the speed of the 5th image in optics with multiple mirrors?

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

I have placed the origin at the middle of the mirrors . This means object is at the origin .

Now I am bit unsure about what the question means with 5th reflection .I am assuming that it means 5th image in either of the mirrors .

I tried to find the distance of the images formed by a mirror , say the one to the right of the origin .

Suppose the two mirrors are at a distance 'x' from the origin .

Consider only one mirror .

First image will be at a distance (from the origin ) = 2x
Second image = 4x
Third image = 8x
Fourth = 12x
Fifth = 16x

Speed of the 5th image = 16dx/dt .

In the question it is given that dx/dt = 5m/s .

Speed of the image = 16×5 = 80m/s .

But this is not an option .

What is the mistake ?

 

[ehild]

Homework Statement

View attachment 224807

Homework Equations

The Attempt at a Solution

I have placed the origin at the middle of the mirrors . This means object is at the origin .

Now I am bit unsure about what the question means with 5th reflection .I am assuming that it means 5th image in either of the mirrors .

I tried to find the distance of the images formed by a mirror , say the one to the right of the origin .

Suppose the two mirrors are at a distance 'x' from the origin .

Consider only one mirror .

First image will be at a distance (from the origin ) = 2x
Second image = 4x
Third image = 8x
Fourth = 12x
Fifth = 16x

Speed of the 5th image = 16dx/dt .

In the question it is given that dx/dt = 5m/s .

Speed of the image = 16×5 = 80m/s .

But this is not an option .

What is the mistake ?

How did you get the distances?

 

[Jahnavi]

I would like to point out that these distances are from the origin , not from the mirror .

Are distances of first two images from the origin correct ?

If image distances are measured from a mirror then ,

First image = x
Second image = 3x
Third image = 7x
Fourth image = 11x
Fifth image = 15x

What does the question mean by 5th reflection ?

If they are counting each reflection from a mirror as 1 reflection then , when first image is formed in each mirror , it accounts for 2 reflection . Strange !

In that case , 5th reflection means when 3rd image is formed in a mirror .

This gives 40m/s , which is one of the options . But this would be a strange interpretation .

 

[haruspex]

First image = x

You previously wrote, correctly, that it is at 2x.
Suppose an image is at k from the origin, beyond the right-hand mirror say. How far is it from the left hand mirror? How far will its reflection be from the left hand mirror? How far will that be from the origin?

 

[Jahnavi]

You previously wrote, correctly, that it is at 2x.

Please note that , in the OP , distances are measured from the origin .

Please also read my above edited post .

 

[Jahnavi]

I realize my mistake .

Thanks !

 

[haruspex]

Please note that , in the OP , distances are measured from the origin .

Yes, I did not notice you had changed that in the later post.