Spherical mirror;find focal length from given data?

[vkash]

Homework Statement

When an object is at distance u₁ and u₂ from pole of concave mirror, images of same size are formed. Find the focal length of the mirror.

Homework Equations

1/v+1/u=1/f

The Attempt at a Solution

Can u please ray diagram for this question. I think their is only one point from which image of size of object form(that's 2f). But it is giving two points. So how to do it..

 

[vela]

I think you're misreading the question. It's not saying the image is the same size as the object. It's saying the image formed when the object is at u₁ is the same size as the image formed when the object is at u₂.

 

[vkash]

I think you're misreading the question. It's not saying the image is the same size as the object. It's saying the image formed when the object is at u₁ is the same size as the image formed when the object is at u₂.

OK!
acha ji.()

but is it possible that two points have same size of image(for a fixed object). I think it will decrease as we take object from pole of the lens to infinity...

please tell me how to proceed..

 

[vela]

Think virtual and real images.

 

[asteriatic]

To find the focal length of a spherical mirror, you can use the equation 1/v + 1/u = 1/f, where v is the image distance, u is the object distance, and f is the focal length. In this case, since the images are of the same size, we can assume that the magnification is 1, so v = u. This means that the equation becomes 1/u + 1/u = 1/f, or 2/u = 1/f. From this, we can solve for f by rearranging the equation to f = u/2. Therefore, the focal length of the mirror is half of the object distance.

As for the ray diagram, it is not necessary to draw one in this case since we are given the information that the images are of the same size. However, if you would like to visualize it, you can draw a ray parallel to the principal axis from the object, and it will reflect through the focal point on the opposite side. This will give you the location of the image, which is at a distance equal to the object distance.