A box is placed 50 cm away from a double convex lens. The image is on the opposite side of the lens, is inverted and 50 cm away from the lens. find:
a)the focal length of the lens.
b)the height of the image.
c) using the focal length that you found, how far from the lens would an image be if the box had been placed 100 cm away?
To find the solutions to 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 distance of the image from the lens (positive for a real image on the opposite side of the lens),
- u is the distance of the object from the lens (positive if the object is on the same side as the incident light).
Let's solve each part step-by-step:
a) To find the focal length of the lens, we need to know the distances of the object and the image from the lens. According to the given information, the object distance (u) is 50 cm, and the image distance (v) is also 50 cm.
Using the lens formula:
1/f = 1/v - 1/u
Substituting the values:
1/f = 1/50 - 1/50
Simplifying:
1/f = 0
Since the denominator becomes zero, this implies that the focal length is infinity. Therefore, the lens is a plano-convex lens.
b) To calculate the height of the image, we need to use the magnification formula:
Magnification (M) = -v/u
Substituting the values:
M = -50/50
Simplifying:
M = -1
The negative sign indicates that the image is inverted. The magnification is 1, meaning the height of the image is the same as the height of the object.
c) Using the focal length we found earlier (infinity/plano-convex lens), we can calculate the new image distance (v') for when the object is 100 cm from the lens (u' = 100 cm).
Using the lens formula:
1/f = 1/v' - 1/u'
Substituting the values:
1/f = 1/v' - 1/100
Since the focal length of the lens is infinite, the equation becomes:
0 = 1/v' - 1/100
Simplifying:
1/v' = 1/100
Taking the reciprocal of both sides:
v' = 100
The new image distance (v') is 100 cm. This means that the image would be located 100 cm away from the lens if the object were placed 100 cm away.
I hope this helps! Let me know if you have any further questions.