(A) The distance between the object and the screen is $D = 90 \; cm$.The distance between the two positions of the lens is $d = 20 \; cm$.The focal le

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(A) The distance between the object and the screen is $D = 90 \; cm$.The distance between the two positions of the lens is $d = 20 \; cm$.The focal length $f$ of the convex lens 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 21.39 \; cm$.Rounding to one decimal place,the focal length is $21.4 \; cm$.

Class 12 Physics Ray Optics and Optical Instruments Refraction by Lenses

Medium

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

A
$21.4$
B
$29.6$
C
$16.8$
D
$34.7$

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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 of the object on the screen is formed by a convex lens at two different locations separated by $20 \; cm$. Determine the focal length (in $cm$) of the lens.

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Focal length of a convex lens is $20 \ cm$ and its refractive index is $1.5$. It produces an erect,enlarged image if the distance of the object from the lens is: (in $cm$)

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