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A student did an experiment with a convex lens. He put an object at different distances 25 cm, 30 cm, 40 cm, 60 cm, and 120 cm from the lens. In each case, he measured the distance of the image from the lens. His results were 100 cm, 24 cm, 60 cm, 30 cm, and 40 cm, respectively. Unfortunately his results are written in wrong order.
(a) Rewrite the image distances in the correct order, (b) What would be the image distance if the object distance was 90 cm?
(c) Which of the object distances gives the biggest image?
(d) What is the focal length of this lens?
(a) The correct order of image distances are: 100 cm, 60 cm, 40 cm, 30 cm, 24 cm.
Explanation
We know that focal length is a constant quantity, so we have to pair the object distance(u) and the image distance(v) such that the focal length always remains the same.
Then, according to the above argument, the correct order of image distances will be 100 cm, 60 cm, 40 cm, 30 cm, 24 cm, because, as the object is carried far from a convex lens, the image is formed closer to the lens.
(b) When u = – 25 cm, v = 100 cm
Lens formula is given by-
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
Substituting the given value we get-
$\frac{1}{f}=\frac{1}{100}-\frac{1}{-25}$
$\frac{1}{f}=\frac{1}{100}+\frac{1}{25}$
$\frac{1}{f}=\frac{1+4}{100}$
$\frac{1}{f}=\frac{5}{100}$
$\frac{1}{f}=\frac{1}{20}$
$f=20cm$
When u = – 90 cm, f = 20 cm (because focal length is a constant quantity), v = ?
Substituting the given value on the lens formula we get-
$\frac{1}{20}=\frac{1}{v}-\frac{1}{-90}$
$\frac{1}{20}=\frac{1}{v}+\frac{1}{90}$
$\frac{1}{20}-\frac{1}{90}=\frac{1}{v}$
$\frac{9-2}{180}=\frac{1}{v}$
$\frac{1}{v}=\frac{7}{180}$
$v=\frac{180}{7}$
$v=25.7cm$
Thus, the image distance will be 25.7 cm, if the object distance was 90 cm.
(c) 25 cm
Explanation
When the object is at the distance of 25 cm, it gives the biggest image because at this position, the object is between f and 2f or, C (centre of curvature), and we know that when an object is placed between f and 2f of a convex lens, we get a real, inverted and magnified image.
(d) 20 cm [As calculated in part (b) of the question]
Updated on: 10-Oct-2022
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