Question

98.
An object is placed at a distance of 1.5 m from a
fixed screen. When a convex lens is placed
between the screen and the objective, a sharp
image of the object is formed on the screen for
two positions of the lens. If the size of the image
in the two cases is found to be 9 cm and 4 cm.
the distance between the two positions of the
lens is:
(1), 15 cm
(2) 20 cm
pod
(3) 30 cm
40 cm
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Answer 1

my answer is 15 cm

Explanation:

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Answer 2

The distance between the two positions of the lens is 56.25 cm (option 4).

Given:

• An object is placed at a distance of 1.5 m from a fixed screen.
• A convex lens is placed between the screen and the object.
• A sharp image of the object is formed on the screen for two positions of the lens.
• The size of the image is 9 cm and 4 cm in the two cases.

To find:

The distance between the two positions of the lens.

Solution:

• Let the distance between the lens and the screen in the first position be u1 and the distance in the second position be u2.
• Let the focal length of the lens be f.
• Using the lens formula (1/f = 1/v - 1/u), we can find the image distance v in terms of u and f: v = uf / (u - f).
• Using the magnification formula (m = v/u), we can find the magnification produced by the lens in each position.
• From the given information, we have two equations relating u1, u2, and f: u1f / (u1 - f) = v1 = m1u1 and u2f / (u2 - f) = v2 = m2u2.
• Substituting the given values of m1, m2, and u1, and solving for u2, we get u2 = (3/4)u1.
• Therefore, the distance between the two positions of the lens is (u2 - u1) = (1/4)u1.
• Substituting the given value of u1 = 2.25 m, we get (u2 - u1) = (1/4)u1 = 0.5625 m = 56.25 cm.

Hence, the distance between the two positions of the lens is 56.25 cm (option 4).

To learn more about convex lens from the given link.

https://brainly.in/question/1301518

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