Comprehension

In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.

Question: 1

The value of \(d\) is

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For the displacement method of a convex lens: \[ f=\frac{D^{2}-d^{2}}{4D} \] This formula is frequently used in practical-based and board examination questions.

Updated On: Jul 2, 2026

\( \sqrt{D(D-4f)} \)
\( \sqrt{D(D-2f)} \)
\( 2\sqrt{Df} \)
\( \sqrt{D(D-f)} \)

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The Correct Option is A

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Question: 2

Compared to the size of the object, the images formed in the two positions of the lens are respectively

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In the displacement method: \[ u_1=v_2 \] and \[ v_1=u_2 \] Thus one image is always diminished while the other is magnified.

Updated On: Jul 2, 2026

reduced, enlarged
reduced, reduced
enlarged, enlarged
enlarged, reduced

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The Correct Option is A

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Question: 3

If the distance between object and screen is \(80.00\) cm and the lens forms sharp images at two positions separated by \(20.00\) cm, the focal length of convex lens is

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For displacement method numericals, directly use \[ f=\frac{D^{2}-d^{2}}{4D} \] This avoids solving separate lens equations and saves considerable time in examinations.

Updated On: Jul 2, 2026

\(15.50\) cm
\(18.75\) cm
\(20.50\) cm
\(22.75\) cm

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The Correct Option is B

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Question: 4

Consider a convex lens of focal length \(15\) cm. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen?

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Always remember the condition for displacement method: \[ D>4f \] where \(D\) is the object-screen distance and \(f\) is the focal length of the convex lens. This is one of the most important results used in practical optics.

Updated On: Jul 2, 2026

\(45\) cm
\(50\) cm
\(55\) cm
\(65\) cm

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The Correct Option is D

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Question: 5

A thin convex lens of focal length \(10\) cm and another thin lens of focal length \(f\) are placed coaxially in contact. If the power of their combination is \(10^3\) D, the value of \(f\) is

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For thin lenses in contact: \[ P=P_1+P_2 \] Always convert focal lengths into metres before calculating power. Remember: \[ P=\frac{1}{f(\text{metre})} \] A convex lens has positive power, while a concave lens has negative power.

Updated On: Jul 2, 2026