A converging lens of focal length 15cm is used to obtain a real image magnified 1/2 times, calculate the distance of the image from the lens
To solve this problem, we can use the lens formula:
1/f = 1/v - 1/u
Here,
f = focal length of the lens = 15 cm
v = distance of the image from the lens (negative since it is a real image)
u = distance of the object from the lens (negative since the object is in front of the lens)
Given that the image is magnified 1/2 times, it means the magnification (m) is equal to 1/2. The magnification can be calculated as:
m = -(v/u)
Substituting the given values, we have:
1/2 = -(v/u)
Simplifying, we get:
u = -2v
Then, substituting this value of u in the lens formula:
1/15 = 1/v + 1/(-2v)
Simplifying, we get:
1/15 = -1/2v
Cross-multiplying, we get:
2v = -15
Dividing both sides by 2, we get:
v = -15/2 = -7.5 cm
Therefore, the distance of the image from the lens is 7.5 cm.