A converging lens of focal length 15cm is used to obtain a real image magnified \(1\frac{1}{2}\) times. Calculate the distance of the image from the lens?
Question 1 Report
A converging lens of focal length 15cm is used to obtain a real image magnified \(1\frac{1}{2}\) times. Calculate the distance of the image from the lens?
Answer Details
The formula for magnification is given as:
magnification = - (image distance) / (object distance)
where magnification is negative for real images.
For a converging lens, the focal length is positive. Using the lens formula:
1/f = 1/u + 1/v
where f is the focal length, u is the object distance, and v is the image distance.
Given that the focal length of the lens is 15cm, the object distance is assumed to be greater than the focal length, since a real image is formed. Also, the magnification is given as 1.5.
Using the formula for magnification, we can rewrite the image distance as:
image distance = - (1.5) x (object distance)
Substituting this into the lens formula:
1/15 = 1/u - 2/3u
Solving for u, we get:
u = 22.5cm
Finally, using the lens formula to find the image distance:
1/15 = 1/22.5 + 1/v
Solving for v, we get:
v = 37.5cm
Therefore, the distance of the image from the lens is 37.5cm.
The correct option is: 37.5cm.
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