A 7·cm tall candle is placed 125·cm from a lens with a focal length of +25·cm. Note: enter the absolute value of your answers for all distances and heights ... use the signs to determine the type and orientation of the images.
a) How far from the lens will the image be?
b) How tall will the image be?
Now, imagine that the candle is moved closer, so that it is only 15·cm from the lens.
d) How far from the lens will the image be?
e) How tall will the image be?
Do it ur self
To solve these questions, 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
We can also use the magnification formula:
m = -v/u
Where:
- m is the magnification of the lens
Now let's solve each part of the question:
a) To find the image distance (v), we need to use the lens formula. Given the object distance (u) as 125 cm and the focal length (f) as +25 cm, we can substitute these values into the formula:
1/25 = 1/v - 1/125
To solve for v, we need to rearrange the equation:
v = 1 / (1/25 - 1/125)
v = 1 / (5/125 - 1/125)
v = 1 / (4/125)
v = 125 / 4
v = 31.25 cm
Therefore, the image will be located 31.25 cm from the lens.
b) To find the image height, we can use the magnification formula. Given that the object height is 7 cm, we can substitute this value into the formula:
m = -v/u
m = -(31.25/125)
m = -0.25
Since the height of the image is negative, it means the image will be inverted. To find the height, we multiply the magnification (m) by the object height:
image height = m * object height
image height = -0.25 * 7
image height = -1.75 cm
Therefore, the height of the image will be 1.75 cm, and it will be inverted.
Now, let's move on to part (d) and (e):
d) Using the same lens formula, we now have a new object distance (u) of 15 cm:
1/25 = 1/v - 1/15
Rearranging the equation to solve for v:
v = 1 / (1/25 - 1/15)
v = 1 / (3/75 - 5/75)
v = 1 / (-2/75)
v = -75/2 = -37.5 cm
Therefore, the image will be located 37.5 cm from the lens.
e) To find the image height using the magnification formula, we can substitute the new values:
m = -v/u
m = -(-37.5/15)
m = 2.5
Since the magnification is positive, it means the image will be upright. We can find the height by multiplying the magnification (m) by the object height:
image height = m * object height
image height = 2.5 * 7
image height = 17.5 cm
Therefore, the height of the image will be 17.5 cm, and it will be upright.