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
(1/p) + (1/q) = 1/f
M = h'/h = -q/p,
Where p is distance of object from lens, q is distance of image from lens, f is focal length of the lens, and M is the magnification
f is positive when the lens is convex:
1/50 + 1/q = 1/15
q = 21.4 cm
M = -21.4/50
To calculate the magnification of the image formed by a lens, we can use the magnification formula:
Magnification (m) = - (image distance)/(object distance)
In this case, the object distance (d_o) is the distance between the candle and the lens, which is 50.0 cm. The image distance (d_i) is the distance between the lens and the image formed by the lens.
To find the image distance, we can use the lens formula:
1/f = 1/d_i - 1/d_o
Here, f is the focal length of the lens, which is 15.0 cm.
Plugging in the values:
1/15.0 cm = 1/d_i - 1/50.0 cm
Simplifying the equation:
1/d_i = 1/15.0 cm + 1/50.0 cm
1/d_i = (50 + 15)/(15 * 50) cm
1/d_i = 65/750 cm
Taking the reciprocal:
d_i = 750/65 cm
Now, we can substitute the values into the magnification formula:
Magnification (m) = - (d_i)/(d_o)
= - (750/65 cm)/(50.0 cm)
Simplifying the equation:
Magnification (m) = - (750/65 cm) / (50.0 cm)
= - (750/65) / (50.0)
≈ -2.327
So, the magnification of the image formed by the lens is approximately -2.33. Therefore, the correct answer is -2.33.