The image of the object formed by a mirror is real, inverted and is of magnification -1. If the image
is at a distance of 40 cm from the mirror, where is the object placed? Where would the image be
if the object is moved 20 cm towards the mirror? State reason and also draw ray diagram for the
new position of the object to justify your answer.
To determine the placement of the object, we can use the mirror equation:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror
- v is the image distance from the mirror
- u is the object distance from the mirror
First, let's analyze the given information:
1. The image formed by the mirror is real and inverted. This means that the image distance (v) will have a negative value.
2. The magnification (m) is -1. Since the image is inverted, the magnification is negative. The magnification formula is given by m = -v/u.
Given:
- v = -40 cm (since the image is 40 cm from the mirror and inverted)
- m = -1
From the magnification formula, we can substitute v = -40 cm and m = -1:
-1 = -(-40)/u
-1 = 40/u
Solving for u, we find:
u = -40 cm
Therefore, the object is placed at a distance of 40 cm from the mirror and on the same side as the image.
Now, let's consider what happens when the object is moved 20 cm towards the mirror. To find the new image position, we can use the magnification formula again:
m = -v/u
Given:
- v' = ? (new image distance)
- m' = -1 (since the image is still inverted)
Substituting the values, we have:
-1 = -v'/u'
We need to find u' when the object is moved 20 cm towards the mirror. This means the new object distance will be:
u' = u - 20 cm
u' = -40 cm - 20 cm
u' = -60 cm
Plugging this into the magnification formula, we get:
-1 = -v' / (-60 cm)
Simplifying, we find:
v' = -60 cm
Therefore, when the object is moved 20 cm towards the mirror, the new image will form at a distance of 60 cm from the mirror, on the same side as the object.
To justify this answer, we can draw a ray diagram.
Start by drawing a vertical line representing the mirror. Place the object above the mirror at a distance of 40 cm (original position). Draw two incident rays from the top and bottom of the object, making them travel parallel to the principal axis. These rays will reflect off the mirror and pass through the focal point.
Now, when the object is moved 20 cm towards the mirror, adjust the position of the object on the diagram (at a distance of 20 cm). Repeat the same process of drawing incident rays and reflecting them off the mirror. The reflected rays will intersect behind the mirror to form a new image at a distance of 60 cm.
By following this method and considering the properties of reflection, we can verify that the new image will form at a distance of 60 cm from the mirror when the object is moved 20 cm towards the mirror.