An object 3-cm high is 20 cm from a concave mirror. The focal length of the mirror is 8 cm.
a. Calculate where the image is located.
b. Calculate the size of the image
To calculate the location of the image formed by a concave mirror, you can use the mirror equation:
1/f = 1/d_o + 1/d_i
Where:
f = focal length of the mirror
d_o = object distance from the mirror
d_i = image distance from the mirror
a. Calculate where the image is located:
Given:
f = 8 cm
d_o = 20 cm
Substitute these values into the mirror equation:
1/8 = 1/20 + 1/d_i
To solve for d_i, we can rearrange the equation:
1/d_i = 1/8 - 1/20
To simplify, find a common denominator:
1/d_i = (20 - 8)/(8 * 20)
= 12/160
= 3/40
Take the reciprocal of both sides to obtain d_i:
d_i = 40/3
Therefore, the image is located approximately 13.33 cm from the mirror (or -13.33 cm since it is on the opposite side of the mirror from the object).
b. Calculate the size of the image:
To calculate the size of the image, we can use the magnification formula:
magnification (m) = -d_i/d_o
Given:
d_i = 40/3
d_o = 20 cm
Substitute these values into the magnification formula:
m = -(40/3) / 20
= -40/60
= -2/3
The negative sign indicates that the image is inverted.
To find the size of the image, multiply the magnification by the height of the object:
size of image = |m| * height of object
= |(-2/3)| * 3 cm
= 2 cm
Therefore, the size of the image formed by the concave mirror is 2 cm.