Image formed by a convex mirror

[Amith2006]

Sir,
1) A man 2 meters tall stands 5 meters in front of a large vertical plane mirror. What is the angle subtended by his image in the mirror at his eye?
I solved it in the following way:
Let AB represent the man and CE represent the mirror mounted on the wall.Here I am assuming that the level of eyes and head are almost the same.
From the figure,
Tan(y) = 2/5
y = 0.38 radians
Is it right?
2) A convergent beam of light converges to a point 20 cm behind the convex mirror on the principal axis. An inverted image of the same size coincident with the virtual object is formed. What is the focal length of the convex mirror?
I didn’t understand this question. Here it is said that an inverted image is formed coincident with the virtual object. But since the image is inverted, it should be real image. At the same time, since the image is coincident with the virtual object, the image also should be virtual isn’t it? How can an image be real as well as virtual? I think the question is wrong. What do you say Sir?

 

[Doc Al]

1) A man 2 meters tall stands 5 meters in front of a large vertical plane mirror. What is the angle subtended by his image in the mirror at his eye?
I solved it in the following way:
Let AB represent the man and CE represent the mirror mounted on the wall.Here I am assuming that the level of eyes and head are almost the same.
From the figure,
Tan(y) = 2/5
y = 0.38 radians
Is it right?

No, not right. Your error is treating the man's image as if it appears at the mirror's surface. But if the man stands 5 meters in front of the mirror, where is his image located?

2) A convergent beam of light converges to a point 20 cm behind the convex mirror on the principal axis. An inverted image of the same size coincident with the virtual object is formed. What is the focal length of the convex mirror?
I didn’t understand this question. Here it is said that an inverted image is formed coincident with the virtual object. But since the image is inverted, it should be real image. At the same time, since the image is coincident with the virtual object, the image also should be virtual isn’t it? How can an image be real as well as virtual? I think the question is wrong. What do you say Sir?

The question is correct. While real images of real objects are inverted, not so for virtual objects. (To convince yourself of this, try drawing a ray diagram of a plane mirror with a virtual object. Is the image real or virtual? Inverted or not?)

 

[Amith2006]

Sir,
Do you mean that the image of a virtual object is virtual and erect always? Is it true only for a convex mirror or for all types of mirrors?

 

[Doc Al]

Do you mean that the image of a virtual object is virtual and erect always?

Of course not. In this example, the image of the virtual object is virtual and inverted.

What I meant was that a real image of a virtual object is erect (not inverted like the real image of a real object).

As I suggested before, play around with a ray diagram of a plane mirror to convince yourself of this. (Plane mirror only because the diagrams are easier to draw.) But any mirror will work.

 

[Amith2006]

Thanks Sir.