Question

A commonplace example of a concave mirror is an ordinary metal spoon. Look at your reflection in the concave surface of a metal spoon; note that it is upside down. If you keep moving the spoon closer, your reflection will flip to being right-side up (your eye may need to be within 1 to 2 cm of the spoon to see this). Your reflection appears to flip not when you are at a distance f from the spoon, but when you are a distance R=2f from the spoon–why is this?

Answer 1

It will be best understood by drawing a ray digram,

note, the fallowing ray diagrams are not draw with perfect ray geometry, they just for visualizatio

In the fallowing figures,

A = Object position

I = Image position

O = Origin

F = focal point of concave mirror ( spoon inner surface inour case )

R = Center of curvature of concave mirror

R = 2.F

The principals of ray diagram for concave mirror are,

1) Incident ray traveling parallel to optical axis after reflection from concave mirror will pass through focal point,

2) Incident ray passing through to center of curvature will reflect back along the same path

3) Incident ray passing through focal point will reflect along the line parallel to optical axis

A)

When the object is located on the left side of center of curvature R the image 'I' will be formed as shown in the image below

B)

When the object is located at the center of curvature R the image 'I' will be formed as shown in the image below

C)

When the object is located between center of curvature R and focal point F  the image 'I' will be formed as shown in the image below

D)

When the object is located at the focal point F there will be no image as shown in the image below

In above image since rays coming from a point on the object will not intersect, there will not be any image.

E)

When the object is located between origin and focal point F the image 'I' will be formed as shown in the image below

In conclusion ,

We see that

When our face is at distance more than the focal distance of the spoon , as per the ray diagrams in parts A, B and C the reflected rays of incident rays coming from a point on our face will converge between spoon and our face and therefore,

there will be real and inverted image formed of our face at distance more than that of focal distance of the spoons concave surface.

When our face is at distance less than the focal distance of the spoon, as per the ray diagram in part E, the reflected rays coming from a point on our face won't br able to converge between spoon and our face,

but the extended rays of reflected rays ( shown by dotted lines in the image in part E ) will converge behind the spoon away from us and therefore,

there will be virtual and upward image formed of our face behind the spoon away from us.