(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

$Assertion (A)$: The focal length of a lens does not change when red light is replaced by blue light.
$Reason (R)$: The focal length of a lens does not depend on the colour of the light used.

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The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

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$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed are

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$A$ thin equiconvex glass lens of refractive index $1.5$ has a power of $5 \,D$. When the lens is immersed in a liquid of refractive index $\mu$, it acts as a divergent lens of focal length $100 \,cm$. The value of $\mu$ of the liquid is:

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$A$ thin lens made of glass of refractive index $1.5$ has a front surface $+ 11 D$ power and back surface $-6 D.$ If this lens is submerged in a liquid of refractive index $1.6,$ the resulting power of the lens is

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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

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$Assertion (A)$: The focal length of a lens does not change when red light is replaced by blue light.$Reason (R)$: The focal length of a lens does not depend on the colour of the light used.

The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed are

$A$ thin equiconvex glass lens of refractive index $1.5$ has a power of $5 \,D$. When the lens is immersed in a liquid of refractive index $\mu$, it acts as a divergent lens of focal length $100 \,cm$. The value of $\mu$ of the liquid is:

$A$ thin lens made of glass of refractive index $1.5$ has a front surface $+ 11 D$ power and back surface $-6 D.$ If this lens is submerged in a liquid of refractive index $1.6,$ the resulting power of the lens is

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$Assertion (A)$: The focal length of a lens does not change when red light is replaced by blue light.
$Reason (R)$: The focal length of a lens does not depend on the colour of the light used.