A concave lens has a focal length 10cm.An object of height 2.5cm is kept at a distance of30cm from the lens .Determine the position of image & its size
Work it out and see
To determine the position of the image formed by a concave lens and its size, we can use the lens formula and magnification formula.
The lens formula is:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens,
- v is the distance of the image from the lens (positive if on the opposite side of the object),
- u is the distance of the object from the lens (negative since the object is on the same side as the incident light).
Given information:
- f = -10 cm (negative for concave lens)
- u = -30 cm (since the object is on the same side as the incident light)
To find v (the distance of the image from the lens), we rearrange the lens formula:
1/v = 1/f + 1/u
1/v = 1/-10 + 1/-30
1/v = -3/30 - 1/10
1/v = -9/30
v = -30/9
v = -3.33 cm
Since the value of v is negative, it tells us that the image is formed on the same side as the object, indicating that it is a virtual image. The negative sign simply indicates the direction in which the image is formed.
To find the size of the image, we can use the magnification formula:
magnification (m) = v/u
Given that:
- u = -30 cm
- v = -3.33 cm
m = (-3.33)/(-30)
m = 0.111
The magnification value of 0.111 indicates that the image formed is reduced in size compared to the object.
Therefore, the position of the image formed by the concave lens is -3.33 cm from the lens (on the same side as the object), and its size is approximately 0.111 times the size of the object.