Image formed by a convex mirror

[Amith2006]

Sir,
I am posting these questions for the 3rd time as you didn't respond. Please respond.
1)A convergent beam of light is incident on a convex mirror of radius of curvature 60 cm as shown in figure. What is the nature and position of the image formed by it?
I solved it in the following way:
Let u, v and f be the object distance, image distance and focal length of the convex mirror respectively.
Here u = + 10 cm, f = +30 cm
1/u + 1/v = 1/f
v = (uf)/(u-f)
= (10 x 30)/(10 – 30)
= -15 cm
Hence the image formed is virtual and 15 cm in front of the mirror. Is it right?
2)A convex mirror of focal length f produces an image (1/n)th of the size of the object. What is the distance of the object from the mirror?
I solved it in the following way:
Magnification = 1/n = -(v/u)
i.e. v = -(u/n)
1/u + 1/v = 1/f
1/u – (n/u) = 1/f
By solving I get,
u = (1-n)f
Are my sign conventions right? Sometimes the diagram may not be clear. So I will try to describe the diagram. A convergent beam of light serves as a virtual object which appears to converge at a distance of 10 cm behind the mirror.

 

[Hootenanny]

The most probably reason at to why no one has answered your question is that your attachments has not yet been approved.

 

[Amith2006]

Sir,
Could anyone online now reply to my query?

 

[Hootenanny]

Question One

There is something wrong here "0" is the object as you suggest in your answer;

Let u, v and f be the object distance, image distance and focal length of the convex mirror respectively.
Here u = + 10 cm,

Surely the mirror should be considered concave?

Question Two

Yes, your sign conventions appear correct.

~H

 

[Amith2006]

Hootenanny Sir,
Why did you feel that the mirror should be concave and not convex? Could you please explain it in detail?

 

[Hootenanny]

Hootenanny Sir,
Why did you feel that the mirror should be concave and not convex? Could you please explain it in detail?

You said in your original post that;

Let u, v and f be the object distance, image distance and focal length of the convex mirror respectively.
Here u = + 10 cm, f = +30 cm

Now if u = +10cm the object should be located at point 0 on your diagram and the rays would be diverging into a concave mirror. Was that diagram given in the question or did you draw it yourself? Would it be possible for you to quote the question as given?

 

[Amith2006]

Sir,
This was the diagram given in the question. Whether the mirror is concave of convex, in both the cases the object will be virtual isn't it, Sir?

 

[Hootenanny]

Sir,
This was the diagram given in the question. Whether the mirror is concave of convex, in both the cases the object will be virtual isn't it, Sir?

Yes, both images would be virtual, however, the convex mirror would lead to an image of reduced size whereas a concave mirror would lead to an enlarged image (as long as the object is inside the focul length of the mirror).