(C) Using the lens formula,we have $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.Here,$u = -OA$ and $v = OB$,so $\frac{1}{f} = \frac{1}{OB} - \frac{1}{-OA

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(C) Using the lens formula,we have $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$.Here,$u = -OA$ and $v = OB$,so $\frac{1}{f} = \frac{1}{OB} - \frac{1}{-OA} = \frac{1}{OB} + \frac{1}{OA} = \frac{OA + OB}{OA \cdot OB}$.Thus,$f = \frac{(OA)(OB)}{OA + OB} = \frac{(OA)(OB)}{AB} \dots(i)$.In the right-angled triangle $\triangle BCA$,$OC$ is the altitude to the hypotenuse $AB$. By the geometric mean theorem in right triangles,$OC^2 = (OA)(OB)$.Substituting this into equation $(i)$,we get $f = \frac{OC^2}{AB}$.

Class 12 Physics Ray Optics and Optical Instruments Refraction by Lenses

If an object is placed at $A$ $(OA > f)$,where $f$ is the focal length of the lens,the image is found to be formed at $B$. $A$ perpendicular is erected at $O$ and $C$ is chosen on it such that the angle $\angle BCA$ is a right angle. Then the value of $f$ will be

A
$AB/OC^2$
B
$(AC)(BC)/OC$
C
$OC^2/AB$
D
$(OC)(AB)/(AC+BC)$

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Class 12 Questions

Class 12

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Ray Optics and Optical Instruments

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Refraction by Lenses

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will

MediumAIPMT 2003

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The radius of the convex surface of a plano-convex lens is $20 \ cm$ and the refractive index of the material of the lens is $1.5$. The focal length of the lens is......$cm$.

Easy

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The size of the images of an object,formed by a thin lens,are equal when the object is placed at two different positions $8 \ cm$ and $24 \ cm$ from the lens. The focal length of the lens is . . . . . . $cm$.

MediumJEE MAIN 2026

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$A$ thin biconvex lens is made of glass $(\mu = 1.50)$ and both surfaces have a radius of curvature of $20 \ cm$. $A$ beam of incident light is parallel to the principal axis of the lens. The lens converges it at a distance $L \ cm$. Then $L = \dots$

Medium

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The focal length of a plano-convex lens is equal to its radius of curvature. Find the refractive index of its material.

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If an object is placed at $A$ $(OA > f)$,where $f$ is the focal length of the lens,the image is found to be formed at $B$. $A$ perpendicular is erected at $O$ and $C$ is chosen on it such that the angle $\angle BCA$ is a right angle. Then the value of $f$ will be

Similar Questions

$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will

The radius of the convex surface of a plano-convex lens is $20 \ cm$ and the refractive index of the material of the lens is $1.5$. The focal length of the lens is......$cm$.

The size of the images of an object,formed by a thin lens,are equal when the object is placed at two different positions $8 \ cm$ and $24 \ cm$ from the lens. The focal length of the lens is . . . . . . $cm$.

$A$ thin biconvex lens is made of glass $(\mu = 1.50)$ and both surfaces have a radius of curvature of $20 \ cm$. $A$ beam of incident light is parallel to the principal axis of the lens. The lens converges it at a distance $L \ cm$. Then $L = \dots$

The focal length of a plano-convex lens is equal to its radius of curvature. Find the refractive index of its material.

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