A convex lens of magnifying glass is held 2.00 cm aove a page to magnify the print. if the image produced by the lens is 3.60 cm away and virtual, what is the focal lenth of the magnifying glass?
To determine the focal length of the magnifying glass, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = distance of the virtual image from the lens
u = distance between the object and the lens
Given:
v = 3.60 cm (distance of the virtual image)
u = 2.00 cm (distance between the object and the lens)
Substituting the given values into the formula:
1/f = 1/3.60 - 1/2.00
Simplifying the equation:
1/f = (2 - 3.60) / (3.60 × 2)
1/f = -1.60 / 7.20
1/f = -0.2222
To find f, we can take the reciprocal of both sides of the equation:
f = -1 / (-0.2222)
f = 4.50 cm
Therefore, the focal length of the magnifying glass is 4.50 cm.
To find the focal length of the magnifying glass, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance
u = object distance
From the given information, we can determine:
v = -3.60 cm (since the image is virtual, the distance is negative)
u = -2.00 cm (the object distance is also negative because it is on the same side as the lens)
Now, we can substitute these values into the lens formula:
1/f = 1/-3.60 - 1/-2.00
Simplifying this equation, we get:
1/f = -1/3.60 + 1/2.00
To add the fractions, we need to find the least common denominator (LCD), which is 3.60. After converting the fractions, the equation becomes:
1/f = -0.28 + 0.50
Adding the values, we get:
1/f = 0.22
Finally, by taking the reciprocal of both sides, we find:
f = 1/0.22
Calculating this value, we get:
f ≈ 4.55 cm
Therefore, the focal length of the magnifying glass is approximately 4.55 cm.