A converging lens ( f = 12.2 cm) is held 7.65 cm in front of a newspaper, the print size of which has a height of 1.88 mm. Find the image distance (in cm) and the height (in mm) of the magnified print.
d =
cm
h =
mm
To find the image distance (d) and the height of the magnified print (h), we can use the magnification formula:
magnification (m) = -image distance (d) / object distance (do)
The magnification formula relates the object distance, image distance, and the size of the object (in this case, the height of the print) with the magnification factor.
Let's calculate the object distance (do) first.
do = object distance = distance from the lens to the newspaper = 7.65 cm
Now we can calculate the magnification (m):
m = -d / do
Given that the focal length of the lens (f) is 12.2 cm, we can use the lens formula:
1/do + 1/di = 1/f
Since the object is placed at a distance of 7.65 cm in front of the lens, the image distance can be calculated as follows:
1/do + 1/di = 1/f
1/7.65 + 1/di = 1/12.2
1/di = 1/12.2 - 1/7.65
Now solve for di:
1/di = (7.65 - 12.2) / (7.65 * 12.2)
di = 1 / ( (7.65 - 12.2) / (7.65 * 12.2) )
di = 23.208 cm (rounded to three decimal places)
Now substitute the calculated values back into the magnification formula to find the magnified print height (h):
m = -d / do
1/(-m) = d / do
Substitute the known values into the formula:
1/(-m) = 23.208 / 7.65
h = 1/(-m) * do
Substitute the known values into the formula:
h = 1/(-m) * 1.88 mm
Now, let's calculate the values.
m = -di / do
m = -23.208 cm / 7.65 cm
m ≈ -3.032 (rounded to three decimal places)
h = 1/(-m) * 1.88 mm
h = 1/(-(-3.032) * 1.88 mm
h ≈ 0.625 mm (rounded to three decimal places)
Therefore, the image distance (d) is approximately 23.208 cm and the magnified print height (h) is approximately 0.625 mm.
To find the image distance (d) and the height of the magnified print (h), we can use the lens formula and the magnification formula.
1. Lens Formula:
The lens formula is given by:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance, and u is the object distance.
Given:
f = 12.2 cm
u = -7.65 cm (negative sign indicates that the object is placed in front of the lens)
Plugging in the values into the lens formula, we can calculate v.
1/12.2 = 1/v - 1/-7.65
Now, solve for v.
2. Magnification Formula:
The magnification formula is given by:
magnification (m) = -v/u
where m is the magnification of the lens.
Plugging in the known values, we can calculate the magnification.
m = -v / -7.65
Now, solve for m.
3. Height Calculation:
The height of the magnified print (h) can be calculated using the magnification formula:
m = h'/h
where h' is the height of the image and h is the height of the object.
Solve for h'.
Now, we have found the image distance (d) and the height (h) of the magnified print.