"If we place two concave both of focal length f mirrors at a distance d facing each other and let source S be midway between so what should be the value of d so that only one image is formed" I have tackling this problem for half an hour now and I got till here: let the first light be hit to mirror 1 on the right the focal length =-f and object distance(u) =-d then image distance(v)=fd/(-d+2f) that the easy part

So if we place object between the pole and focus then image will be virtual

And if we place the object at centre of curvature the image will be formed at centre of curvature

I think placing it between the focus and centre of curvature will result in multiple reflection which is not allowed

@JohnRennie

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@alam Hi

Hi

I think I should let image be formed at centre of curvature

I guess it depends on what you mean by only one image.

Suppose the distance between the mirrors is 2R i.e. 4f.

By only one image I think only one reflection

At the case where it does not gets reflected to another mirror

So you do get multiple reflections, but all the images are at the same place.

So that could be a solution.

Yes I do get another reflection if I keep it at centre of curvature

Which is not allowed

If I keep it between the pole and focus I get virtual image

Wait then we don't get another reflection if the image itself is virtual

OK. Now suppose the distance between the mirrors is R i.e. 2f.

Ok

Yes

Then the parallel rays hit the second mirror, and they form an image at the focal point of the second mirror i.e. at the same place as the original object.

So again the object and image coincide, but this time the two reflections produced only a single image.

yeah you're right

So there are two solutions to the problem. It's just a question of what exactly the question is asking.

Yes there are two solution that is 2f and 4f are values of d

In answer

OK :-)

So I guess the question just means that the images have to be in the same place as the object, and it doesn't matter how many images are formed as long as they are all in the same place.

Yes

I got it thanks

OK :-)

You're goat