A 3 cm flower is placed 40 cm from a converging lens with a focal length of 15 cm. What are the orientation, size and type of the image?
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)=
=0.4•0.15/(0.4-0.15)=0.24 m,
0.03/0.4 =h/ d₁ ,
h= d₁•0.03/0.4=0.24•0.03/0.4=0.018 m
To determine the orientation, size, and type of the image formed by a lens, we need to use the lens formula and magnification formula.
The lens formula is given by:
1/f = 1/v - 1/u
Where,
f = focal length of the lens
v = image distance
u = object distance
In this case, the lens is converging, so the focal length (f) would be positive. The object distance (u) is the distance of the flower from the lens, which is given as 40 cm.
To find the image distance (v), we can rearrange the lens formula as:
1/v = 1/f - 1/u
Next, we need to find the magnification formula:
magnification (m) = -v/u
The size and type of the image can be determined using the magnification value:
- If the magnification (m) is positive, the image is upright.
- If the magnification (m) is negative, the image is inverted.
- If the magnification (m) is greater than 1, the image is magnified.
- If the magnification (m) is less than 1, the image is reduced.
- If the magnification (m) is equal to 1, the image is the same size as the object (neither magnified nor reduced).
Let's calculate the values.
Given:
Focal length (f) = 15 cm
Object distance (u) = 40 cm
Using the lens formula:
1/v = 1/f - 1/u
1/v = 1/15 - 1/40
Simplifying the equation:
1/v = (40 - 15)/600
1/v = 25/600
v = 600/25
v = 24 cm
Now, let's calculate the magnification:
Magnification (m) = -v/u
m = -(24/40)
m = -0.6
From the magnification value:
- The image is inverted since the magnification is negative.
- The image is reduced since the magnification is less than 1.
To determine the size of the image, we can use the magnification formula. Since the object size is given as 3 cm, we can multiply it by the magnification value to find the image size:
Image size = Object size × Magnification
Image size = 3 cm × (-0.6)
Image size = -1.8 cm
So, the orientation of the image is inverted, the size of the image is 1.8 cm, and it is reduced.