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?
1.50 cm
3.00 cm
6.00 cm
9.00 cm
I honestly don't even know where to begin with this one, but if I guessed, I would go with 1.50cm
6.00 cm
Thank you so much!
To solve this problem, you can use the lens equation:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens
- do is the object distance (distance of the candle from the lens, taken as positive)
- di is the image distance (distance of the image from the lens, taken as positive if the image is on the opposite side of the object)
In this case, the focal length (f) is given as 15.0 cm, and the object distance (do) is given as 30.0 cm.
Let's solve for the image distance (di). First, substitute the given values into the lens equation:
1/15.0 = 1/30.0 + 1/di
Now, solve for di:
1/di = 1/15.0 - 1/30.0
1/di = (2 - 1)/30.0
1/di = 1/30.0
Multiply both sides by 30.0:
di = 30.0 cm
The image distance (di) is 30.0 cm.
Now, to find the height of the image, we can use the magnification equation:
magnification = -di/do
In this case, the object height is given as 6.00 cm and the height of the image is unknown.
Let's solve for the height of the image:
magnification = -30.0/30.0
Simplifying, magnification = -1.
magnification = image height/object height
Rearrange the equation to solve for the image height:
image height = magnification * object height
image height = -1 * 6.00 cm
The image height is -6.00 cm. Note that the negative sign indicates an inverted image.
Therefore, none of the given options (1.50 cm, 3.00 cm, 6.00 cm, 9.00 cm) are correct. The correct answer is not provided.