A 6.00 cm tall candle is placed at a distance of 30.0 cm from a double convex lens having a focal length of 15.0 cm. How tall is the image?
To determine the height of the image formed by a lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the image distance from the lens,
- u is the object distance from the lens.
In this case, the lens is double convex and has a focal length of 15.0 cm. The object distance, u, is the distance from the candle to the lens, which is given as 30.0 cm.
To find v, the image distance from the lens, we can rearrange the lens formula as follows:
1/v = 1/f - 1/u
Plugging in the values:
1/v = 1/15 - 1/30
Simplifying:
1/v = (2 - 1)/30
1/v = 1/30
v = 30 cm
Now that we know the image distance, we can calculate the magnification (m) using the formula:
m = -v/u
Plugging in the values:
m = -30/30
m = -1
The negative sign indicates that the image is inverted.
Finally, to find the height of the image, we can use the magnification formula:
m = -h'/h
where:
- h' is the height of the image,
- h is the height of the object (candle).
Rearranging the formula:
h' = -m * h
Plugging in the values:
h' = -(-1) * 6.00 cm
h' = 6.00 cm
Therefore, the height of the image formed by the double convex lens is 6.00 cm.