An object 3 cm is high is placed 24 cm away from a convex lens of focal length 8 cm. Find nature position and height of the image?
help plesase
To find the nature position and height of the image formed by a convex lens, 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 (positive if the image is real, negative if the image is virtual),
- u is the object distance from the lens (positive if the object is on the same side as the incident light, negative if the object is on the opposite side of the incident light).
We are given:
- object distance u = 24 cm,
- focal length f = 8 cm.
We need to find:
- image distance v,
- nature (real/virtual) of the image,
- height of the image.
Now we can substitute the given values into the lens formula and solve for v.
1/8 = 1/v - 1/24
To solve the equation, let's first find the least common denominator:
1/8 = (3 - v) / (3v)
Now cross multiply:
3v = 24(3 - v)
3v = 72 - 24v
3v + 24v = 72
27v = 72
v = 72 / 27
v ≈ 2.67 cm
Now, to find the nature of the image, we can determine whether the image distance (v) is positive or negative. If v is positive, the image is real. If v is negative, the image is virtual.
In this case, since v is positive (approximately 2.67 cm), the image formed by the lens is real.
Next, let's find the height of the image. We can use the magnification formula:
magnification (m) = height of the image (h') / height of the object (h)
The magnification (m) for a convex lens is given by:
m = -v / u
Substituting the given values:
m = -(2.67 cm) / (24 cm)
m ≈ -0.111
The height of the image can be found by multiplying the magnification (m) by the height of the object (h).
h' = m * h
Substituting the given height of the object (h = 3 cm):
h' ≈ (-0.111) * (3 cm)
h' ≈ -0.333 cm
The negative sign indicates that the image formed by the convex lens is inverted. The height of the image is approximately -0.333 cm.