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 lens, you can use the formula:
Magnification (m) = - (image distance / object distance)
In this case, the object distance is the distance between the candle and the lens, which is 50.0 cm. The image distance can be determined using the lens formula:
1 / focal length = 1 / object distance + 1 / image distance
where the focal length is given as 15.0 cm. Rearranging the equation, we have:
1 / image distance = 1 / focal length - 1 / object distance
Substituting the values, we get:
1 / image distance = 1 / 15.0 cm - 1 / 50.0 cm
Calculating the right-hand side:
1 / image distance = 0.067 + 0.02
1 / image distance = 0.087
image distance = 1 / 0.087
image distance ≈ 11.5 cm
Now, we can plug in the values for the image and object distances in the magnification formula:
m = - (11.5 cm / 50.0 cm)
Calculating:
m ≈ -0.23
Therefore, the magnification of the image formed by the lens is approximately -0.23. However, none of the given options match this result exactly.