(A) For a convex lens,the lens formula is given by $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.Using sign convention,$u$ is negative,so let $u = -|u|$ a

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(A) For a convex lens,the lens formula is given by $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.Using sign convention,$u$ is negative,so let $u = -|u|$ and $v = |v|$.The equation becomes $\frac{1}{|v|} - \frac{1}{-|u|} = \frac{1}{f}$,which simplifies to $\frac{1}{|v|} + \frac{1}{|u|} = \frac{1}{f}$.$A$ straight line passing through the origin making an angle of $45^{\circ}$ with the $x$-axis has the equation $|v| = |u|$.At the intersection point $P$,we substitute $|v| = |u|$ into the lens formula:$\frac{1}{|u|} + \frac{1}{|u|} = \frac{1}{f}$$\frac{2}{|u|} = \frac{1}{f}$$|u| = 2f$.Since $|v| = |u|$,we have $|v| = 2f$.Thus,the coordinates of point $P$ are $(2f, 2f)$.

Class 12 Physics Ray Optics and Optical Instruments Refraction by Lenses

Difficult

In an optics experiment,with the position of the object fixed,a student varies the position of a convex lens and for each position,the screen is adjusted to get a clear image of the object. $A$ graph between the object distance $|u|$ and the image distance $|v|$,from the lens,is plotted using the same scale for the two axes. $A$ straight line passing through the origin and making an angle of $45^{\circ}$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be

AIEEE 2009 All AIEEE

A
$(2f, 2f)$
B
$(f/2, f/2)$
C
$(f, f)$
D
$(4f, 4f)$

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Ray Optics and Optical Instruments

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Refraction by Lenses

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An object and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?

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If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on the left of the lens is at

EasyTS EAMCET 2020

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$A$ convex lens of focal length $0.15 \,m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid, its focal length is increased by $0.225 \,m$. The refractive index of the liquid is

DifficultAP EAMCET 2002

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The magnitudes of power of a biconvex lens (refractive index $1.5$) and that of a plano-concave lens (refractive index $= 1.7$) are same. If the curvature of the plano-concave lens exactly matches with the curvature of the back surface of the biconvex lens, then the ratio of the radius of curvature of the front and back surface of the biconvex lens is . . . . . . .

DifficultJEE MAIN 2026

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$A$ convex lens of focal length $30 \,cm$ produces $5$ times magnified real image of an object. What is the object distance (in $\,cm$)?

EasyWBJEE 2011

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If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on the left of the lens is at

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