1. An object of length 200cm is photographed when it is 100cm from the hole.if the distance from the pinhole to the screen is 10cm.calculate the length of the image and magnification.
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Please i need the calculation of the length of the image and magnification
An object of length 200cm is photographed when it is 100cm from the hole.if the distance from the pinhole to the screen is 10cm.calculate the length of the image and magnification.
I need answers
To calculate the length of the image and the magnification, we can make use of the thin lens formula and the magnification formula.
Let's start with the thin lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
In this case, the lens is the pinhole, which is considered a special case where the focal length is effectively infinite. Therefore, we can treat the focal length (f) as a very large number or infinity, which simplifies the formula to:
1/v = 1/u
Given that the object distance (u) is 100 cm from the hole and the distance from the hole to the screen (v) is 10 cm, we can calculate the image distance (v):
1/v = 1/u
1/v = 1/100
v = 100 cm
So, the image distance (v) is 100 cm.
Now let's calculate the length of the image. We can use the following formula:
magnification (m) = height of the image (h_i) / height of the object (h_o)
Since we are given the length of the object (200 cm), we can use the length to represent the height of both the image and object. So, the magnification formula becomes:
m = h_i / h_o = length of the image / length of the object
Plugging in the values we have:
m = h_i / h_o = length of the image / length of the object
m = h_i / 200
To find the length of the image (h_i), we can rearrange the formula:
h_i = m * h_o
Given that the magnification (m) is equal to the image distance (v) divided by the object distance (u):
m = v / u
m = 100 / 100
m = 1
Therefore, the magnification (m) is 1.
Now, substituting the values into the equation:
h_i = m * h_o
h_i = 1 * 200
h_i = 200 cm
So, the length of the image (h_i) is 200 cm, which is equal to the length of the object (h_o).
To summarize:
- The length of the image is 200 cm.
- The magnification is 1.