(A) For a fixed distance $D$ between the object and the screen,a convex lens of focal length $f$ forms a sharp image at two positions if $D > 4f$.Let

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(A) For a fixed distance $D$ between the object and the screen,a convex lens of focal length $f$ forms a sharp image at two positions if $D > 4f$.Let $D = 90 \ cm$ and the separation between the two lens positions be $d = 20 \ cm$.The focal length $f$ is given by the displacement method formula:$f = \frac{D^2 - d^2}{4D}$Substituting the given values:$f = \frac{90^2 - 20^2}{4 \times 90}$$f = \frac{8100 - 400}{360}$$f = \frac{7700}{360}$$f = \frac{770}{36} \approx 21.38 \ cm$.

Class 12 Physics Ray Optics and Optical Instruments Refraction by Lenses

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$A$ screen is placed $90 \ cm$ from an object. The image is formed on the screen by a convex lens placed at two different locations separated by $20 \ cm$. The focal length of the lens is approximately equal to: (in $cm$)

TS EAMCET 2021 All TS EAMCET

A
$21.38$
B
$30.0$
C
$35.0$
D
$24$

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Ray Optics and Optical Instruments

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Refraction by Lenses

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$A$ screen is placed $90 \ cm$ from an object. The image is formed on the screen by a convex lens placed at two different locations separated by $20 \ cm$. The focal length of the lens is approximately equal to: (in $cm$)

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