Article about Image formation by the convex mirror

To understand the formation of image by the convex mirror, learn the example problems and solution below. In this case, an object is assumed to be at a certain distance from the convex mirror,

then draw the image formation by the convex mirror, the image distance from the convex mirror and the magnification of image by the convex mirror.

Suppose a convex mirror has a radius of 30 cm. Draw the image formation then determine the image distance and the magnification of the image, if:

a) The object distance is smaller than the focal length (do < f)

b) The object distance is the same as the focal length (do = f)

c) The object distance is greater than the focal length and smaller than the radius of the curvature of the mirror (f < do <r)

d) The object distance is the same as the radius of the curvature of the mirror (do = R)

e) The object distance is greater than the radius of curvature of the mirror (do > R)

__Known :__

The radius of curvature of the convex mirror (R) = 30 cm

The focal length of the convex mirror (f) = R / 2 = 30/2 = -15 cm

The focal point is behind the convex mirror, where the beam of light does not pass through the focal point. Therefore, the focus of the convex mirror is given a negative sign.

__Solution :__

**The object distance is smaller than the focal length of the convex mirror (do < f)**

Suppose the object distance from the mirror is 5 cm and 10 cm.

The focal length (f) = -15 cm and if the object distance (d

_{o}) = 5 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/s = -1/15 – 1/5 = -1/15 – 3/15 = -4/20

di = -20/4 = -5 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the mirror, where the beam of light does not pass through the image.*

*The image distance (di) 5 cm equals to the object distance (d) 5 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-5)/5 = 5/5 = 1 time

*The linear magnification of the image (M) 1 means the size of the image equals to the size of the object.*

*The linear magnification of the image (M) has a positive sign, means the image is upright.*

The focal length (f) = -15 cm and if the object distance (do) = 10 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/10 = -2/30 – 3/30 = -5/30

di = -30/5 = -6 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the convex mirror, where the beam of light does not pass through the image.*

*The image distance (di) 6 cm is smaller than the object distance (do) 10 cm.*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-6)/10 = 6/10 = 0.6 times

*The linear magnification of the image (M) is smaller than 1 means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign means that the image is upright.*

**The object distance is the same as the focal length of the convex mirror (do = f)**

The focal length (f) = the object distance (do) = 15 cm.

__The image distance (di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/15 = -2/15

di = -15/2 = -7.5 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the convex mirror, where the beam of light does not pass through the image.*

*The image distance (di) 7.5 cm is smaller than the object distance (do) 15 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-7,5)/15 = 7.5 / 15 = 0.5 times

*The linear magnification of the image (M) is smaller than 1 means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign, means the image is upright.*

**The object distance is greater than the focal length and smaller than the radius of curvature of the convex mirror (f < do <R)**

Suppose the object distance from the mirror is 20 cm and 25 cm.

The focal length (f) = -15 cm and if the object distance (do) = 20 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/20 = -4/60 – 3/60 = -7/60

di = -60/7 = -8.6 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the convex mirror where the beam of light does not pass through the image.*

*The image distance (di) 8.6 cm is smaller than the object distance (do) 20 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-8.6)/20 = 8.6 / 20 = 0.4 times

*The linear magnification of the image (M) is smaller than 1, means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign means that the image is upright.*

The focal length (f) = -15 cm and if the object distance (do) = 25 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/25 = -25/375 – 15/375 = -35/375

di = -375/35 = -10.7 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the concave mirror, where the beam of light does not pass through the image.*

*The image distance (di) 10.7 cm, smaller than the object distance (do) 25 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-10.7) / 25 = 10.7 / 25 = 0.4 times

*The linear magnification of the image (M) is smaller than 1 means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign means that the image is upright.*

**The object distance is equal to the radius of curvature of the convex mirror (do = R)**

The radius of curvature of the mirror (R) = the object distance (do) = 30 cm.

__The image distance ____(____di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/30 = -2/30 – 1/30 = -3/30

di = -30/3 = -10 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the convex mirror, where the beam of light does not pass through the image.*

*The image distance (di) 10 cm, smaller than the object distance (do) 30 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-10)/30 = 1/3

*The linear magnification of the image (M) is smaller than 1, means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign means that the image is upright.*

**The object distance is greater than the radius of curvature of the convex mirror (do > R)**

Suppose the object distance from the mirror is 40 cm and 50 cm.

The focal length (f) = -15 cm and if the object distance (do) = 40 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/do = -1/15 – 1/40 = -8/120 – 3/120 = -11/120

di = -120/11 = -10.9 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind the convex mirror where the beam of light does not pass through the image.*

*The image distance (di) 10.9 cm, smaller than the object distance (do) 40 cm*

__The linear magnification of the image (____M)__ :

M = -di / do = -(-10.9) / 40 = 10.9 / 40 = 0.3 times

*The linear magnification of the image (M) has a positive sign means that the image is upright.*

The focal length, f) = -15 cm and the object distance (do) = 50 cm

__The image distance ____(____di____)__ :

1/di = 1/f – 1/di = -1/15 – 1/50 = -10 / 150 – 3 / 150 = -13 / 150

di = -150/13 = -11.5 cm

*The image distance (di) has a negative sign means that the image is virtual, or the image is behind a convex mirror, where the beam of light does not pass through the image.*

*The image distance (in) 11.5 cm, smaller than the object distance (do) 50 cm*

__The linear magnification of the image ____(M)__ :

M = -di / do = -(-11.5) / 50 = 11.5 / 50 = 0.2 times

*The linear magnification of the image (M) is smaller than 1, means that the size of the image is smaller than the size of the object.*

*The linear magnification of the image (M) has a positive sign, means the image is upright.*