An object is placed at a distance of 50cm from a convex lens of fical length 20cm .find the nature and position of yhe subject.
To find the nature and position of the object placed in front of 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,
- u is the object distance from the lens.
In this case, the focal length of the convex lens is given as 20cm and the object distance (u) is 50cm.
By substituting these values into the formula, we can find the image distance (v), which will help us determine the nature and position of the object.
1/20 = 1/v - 1/50
Simplifying the equation:
1/v = 1/20 + 1/50
To add these fractions, we need to find their LCD (Least Common Denominator) which is 100. The equation becomes:
1/v = (5/100) + (2/100)
1/v = 7/100
Now, taking the reciprocal of both sides:
v/1 = 100/7
Simplifying, the value of v is approximately 14.29 cm.
Now that we have the image distance (v), we can analyze it to find the nature and position of the object:
1. If v is positive: The image is formed on the opposite side of the lens as the object.
2. If v is negative: The image is formed on the same side of the lens as the object.
In this case, the value of v is positive, indicating that the image is formed on the opposite side of the lens as the object.
Additionally, the nature of the image can be determined by the magnification:
magnification (m) = -v/u
Substituting the values, we have:
m = -14.29/50
m = -0.286
Since the magnification is negative, the image formed is inverted.
Therefore, the answer is:
- The nature of the image formed by the convex lens is inverted.
- The position of the image is approximately 14.29 cm on the opposite side of the lens from the object.