A convex lens of focal length 2.5 cm is placed 4 cm from a small object of height 4 cm. Use a ruler and construct the image. Is the image real or virtual, upright or inverted? What is the image distance? What is the height of the image? What is the magnification?
The object located between F and 2F => the image will be located beyond the 2F point on the other side of the lens. It is real, inverted and its dimension is larger than the object demension.
d₀ - object distance
d₁ - image distance
f- focal lenth
1/d₀ +1/d₁ =1/f
1/d₁ =1/f - 1/d₀ =
= (d₀-f)/ d₀•f
d₁=d₀•f/(d₀-f)=0.04•0.025/(0.04-0.025) = 0.067 m
h₀/d₀=h₁/d₁
h₁= d₁•h₀/d₀=0.067•0.04/0.04 = 0.067 m
To determine the characteristics of the image formed by a convex lens, we can use the lens formula and 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:
focal length (f) = 2.5 cm
object distance (u) = 4 cm
Substituting these values into the lens formula, we can find the image distance (v).
1/2.5 = 1/v - 1/4
Simplifying the equation, we get:
1/v = 1/2.5 + 1/4
1/v = (4 + 2.5)/(2.5 * 4)
1/v = 6.5/10
v = 10/6.5
v ≈ 1.54 cm
Therefore, the image distance is approximately 1.54 cm.
2. Magnification Formula:
The magnification (m) is given by:
m = -v/u
Substituting the values of v and u, we can calculate the magnification.
m = -1.54/4
m ≈ -0.385
The negative value indicates that the image is inverted.
3. Image Characteristics:
- Real or Virtual: Since the image is formed on the opposite side of the lens, it is real.
- Upright or Inverted: The negative magnification value indicates that the image is inverted.
- Image distance: The image distance is approximately 1.54 cm.
- Height of the image: To determine the height of the image, we can use the magnification formula.
m = h'/h
where h' is the height of the image and h is the height of the object.
Given:
height of the object (h) = 4 cm
m = -0.385
Rearranging the formula, we get:
h' = m * h
h' = -0.385 * 4
h' ≈ -1.54 cm
The negative sign indicates that the image is inverted.
Therefore, the height of the image is approximately 1.54 cm.
To construct the image to scale using a ruler, mark a point 4 cm from the lens to represent the object. From this point, draw a line that passes through the center of the lens (this is the principal axis). The image distance (1.54 cm) can be measured from this lens along the principal axis. At this point, mark a point to represent the image.
Using the same scale, draw a line connecting the top of the object to the image point. The length of this line represents the height of the image (approximately 1.54 cm).
By following these steps, you can construct the image on paper using a ruler and determine its characteristics.