A 2cm tall object is placed perpendicular to principle axis of a convex lence of focal length 10cm. The distance of object from lence is 15cm. Find nature of position and size of image. Also find its magnification
To find the nature of the position and size of the image, as well as the magnification, we can use the lens formula and magnification formula.
Lens formula:
1/f = 1/v - 1/u
Magnification formula:
magnification (m) = -v/u
Where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
Given:
f = 10 cm
u = -15 cm (since the object is placed on the other side of the lens)
Height of the object (h) = 2 cm
First, let's find the image distance (v) using the lens formula:
1/f = 1/v - 1/u
Since the object is placed on the other side of the lens, u = -15 cm.
Substituting the values:
1/10 = 1/v - 1/-15
1/10 = (15 - v)/(-15v)
Cross-multiplying:
v = -150/7 cm
The negative sign indicates that the image is formed on the same side as the object, which means the image is virtual.
Next, let's find the magnification (m) using the magnification formula:
m = -v/u
Substituting the values:
m = -(-150/7) / -15
m ≈ -1.43
The negative magnification indicates an inverted image.
Now, let's find the size of the image.
Size of the image (h') / height of the object (h) = magnification (m)
Substituting the values:
h' / 2 = -1.43
h' ≈ -2.86 cm
The negative sign indicates that the image is inverted compared to the object.
To summarize:
- The nature of the position of the image is virtual.
- The nature of the size of the image is inverted.
- The magnification of the image is approximately -1.43.
- The size of the image is approximately -2.86 cm.
To determine the nature of the position and size of the image formed by a convex lens, we can use the lens formula and magnification formula.
Given:
Height of the object (h₁) = 2 cm
Focal length of the lens (f) = 10 cm
Distance of the object from the lens (u) = 15 cm
1. Calculate the image distance (v) using the lens formula: 1/v - 1/u = 1/f
Substituting the values:
1/v - 1/15 = 1/10
1/v = 1/10 + 1/15
1/v = 3/30 + 2/30
1/v = 5/30
v = 30/5
v = 6 cm
2. Calculate the magnification (M) using the formula: M = -v/u
Substituting the values:
M = -6/15
M = -2/5
Now, based on the computed values:
- The negative magnification (M) indicates that the image is inverted.
- The positive image distance (v = 6 cm) shows that the image is formed on the opposite side as the object (real image).
- As the magnification (M = -2/5) is less than 1, the image is smaller than the object in size.
Therefore, the nature of the position and size of the image formed by the convex lens is:
- Position: Real image formed on the opposite side of the object.
- Size: The size of the image is smaller than the object.
- Magnification: The magnification is -2/5, indicating an inverted and diminished image.