An object 29.0 mm high is 27.0 cm away from a concave spherical mirror with a radius of curvature of 28.0 cm. How do i get these answers?
a)How far from the mirror is the image? (absolute distance) answer 29.1cm
b)What is the absolute size of the image? answer 3.12 cm
Follow the procedute I explained in an earlier answer today:
http://www.jiskha.com/display.cgi?id=1274110901
To find the distance of the image from the mirror (absolute distance), you can use the mirror formula. The mirror formula is given by:
1/f = 1/v + 1/u
Where:
f = focal length of the mirror
v = distance of the image from the mirror (virtual image considered positive)
u = distance of the object from the mirror (real objects considered negative)
Step 1: Convert the given measurements to meters for consistent units:
Object height (h) = 29.0 mm = 29.0/1000 = 0.029 meters
Object distance (u) = 27.0 cm = 27.0/100 = 0.27 meters
Radius of curvature (R) = 28.0 cm = 28.0/100 = 0.28 meters
Step 2: Calculate the focal length (f) of the mirror using the formula:
f = R/2
= 0.28/2
= 0.14 meters
Step 3: Substitute the values into the mirror formula and solve for the image distance (v):
1/f = 1/v + 1/u
1/0.14 = 1/v + 1/0.27
7.1429 = 1/v + 3.7037
1/v = 7.1429 - 3.7037
1/v = 3.4392
v = 1/3.4392
v ≈ 0.291 meters
To convert the image distance from meters to centimeters:
v = 0.291 x 100
v ≈ 29.1 cm
Therefore, the image is approximately 29.1 cm away from the mirror (absolute distance).
To find the absolute size of the image, you can use the magnification formula:
magnification (m) = height of the image (h') / height of the object (h)
Step 1: Substitute the given measurements into the magnification formula:
m = h' / h = v / u
Step 2: Calculate the magnification:
m = 0.291 / 0.27 ≈ 1.076
Step 3: Find the height of the image (h') using the magnification formula:
h' = m * h
h' = 1.076 * 0.029
h' ≈ 0.0312 meters
To convert the height of the image from meters to centimeters:
h' = 0.0312 x 100
h' ≈ 3.12 cm
Therefore, the absolute size of the image is approximately 3.12 cm.