A 5.00 cm tall candle is placed at a distance of 50.0 cm from a double convex lens having a focal length of 15.0 cm. What is the magnification of the image?
-0.429
-2.33
0.429
2.33
To calculate the magnification of the image formed by a double convex lens, we can use the formula:
magnification (m) = - (image height / object height)
First, let's find the image height using the lens formula:
1/f = 1/di - 1/do
where f is the focal length, di is the image distance, and do is the object distance.
Given:
Object height (ho) = 5.00 cm
Object distance (do) = 50.0 cm
Focal length (f) = 15.0 cm
Using the lens formula, we can find the image distance (di):
1/15 = 1/di - 1/50
Solving this equation, we can find di.
1/di = 1/15 - 1/50
1/di = (50 - 15) / (15 * 50)
1/di = 35 / (15 * 50)
1/di = 7 / (3 * 10)
di = (3 * 10) / 7
di = 30 / 7
di ≈ 4.29 cm
Now, we can substitute the image distance (di) into the magnification formula:
magnification (m) = - (image height / object height)
To find the image height, we can use the magnification formula in terms of object and image distance:
magnification (m) = - (hi / ho) = - (di / do)
Substituting the values:
m = - (4.29 cm / 50.0 cm)
m ≈ -0.0858
So, the magnification of the image is approximately -0.0858.