A concave mirror has a focal length of 20 cm. What is the magnification of an object placed 128 cm in front of this mirror?
To find the magnification of an object placed in front of a concave mirror, you can use the magnification formula:
Magnification = - (Image distance/Object distance)
In this case, the object distance (u) is given as 128 cm, and the focal length (f) is given as 20 cm.
First, let's find the image distance (v).
Using the mirror equation:
1/f = 1/v - 1/u
Substituting the given values:
1/20 = 1/v - 1/128
Simplifying:
1/20 = (128 - v)/128v
Cross-multiplying:
128v = 20(128 - v)
128v = 2560 - 20v
148v = 2560
v = 2560/148
v ≈ 17.3 cm
Now, we can calculate the magnification:
Magnification = - (v/u)
Magnification = - (17.3/128)
Magnification ≈ -0.135
Therefore, the magnification of the object is approximately -0.135.
To calculate the magnification of an object placed in front of a concave mirror, we can use the formula:
Magnification (m) = - (image distance) / (object distance)
Given that the focal length (f) of the concave mirror is 20 cm, we need to calculate the object distance (u), which is 128 cm in this case.
Using the mirror equation for concave mirrors:
1/f = 1/v - 1/u
Where:
f = focal length
v = image distance
u = object distance
Rearranging the formula, we get:
1/v = 1/f + 1/u
Plugging in the given values, we have:
1/v = 1/20 + 1/128
Simplifying this equation:
1/v = (128 + 20) / (20 * 128)
1/v = 148 / 2560
v = 2560 / 148
v = 17.30 cm
Now we can calculate the magnification (m):
m = - (v / u)
m = - (17.30 / 128)
m ≈ -0.135
Therefore, the magnification of the object placed 128 cm in front of the concave mirror is approximately -0.135.