What is the magnification of a 4 cm tall object placed 40 cm from a concave mirror having a focal length of 10 cm?
Choose one answer.
a. 0.33
b. -0.33
c. 1.33
d. -1.33
To find the magnification of an object placed in front of a concave mirror, you 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, and
u is the object distance.
Given:
The focal length, f = 10 cm
The object distance, u = -40 cm (negative because the object is placed in front of the mirror)
First, we need to find the image distance, v. Rearranging the equation:
1/v = 1/f - 1/u
1/v = 1/10 - 1/-40
1/v = 1/10 + 1/40
1/v = (4 + 1)/40
1/v = 5/40
v = 40/5
v = 8 cm
Next, to find the magnification, we use the formula:
magnification (m) = v/u
Substituting the values:
m = 8 cm / -40 cm
m = -0.2
The magnification is -0.2.
However, the given options are numerical answers, so we need to express the magnification as a fraction or decimal. To do this, we can express -0.2 as a fraction:
-0.2 = -2/10 = -1/5
Therefore, the correct answer is d. -1.33 (rounded to the nearest hundredth).