(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

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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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Class 12

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Ray Optics and Optical Instruments

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Refraction by Lenses

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AIEEE 2009 Paper All AIEEE years →

An object is moving with a velocity $V_O = 4 \text{ cm/sec}$ towards a convex lens of focal length $f = 10 \text{ cm}$. The lens is also moving with a velocity $V_L = 2 \text{ cm/sec}$ in the same direction. At the instant when the object is at a distance of $30 \text{ cm}$ from the lens,find the velocity of the image.

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If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

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When blue light is used instead of red light in a convex lens,its focal length will ......... .

Medium

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$A$ rod of length $2 \text{ cm}$ makes an angle of $\frac{2 \pi}{3} \text{ rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10 \text{ cm}$ and is placed at a distance of $\frac{40}{3} \text{ cm}$ from the object as shown in the figure. The height of the image is $\frac{30 \sqrt{3}}{13} \text{ cm}$ and the angle made by it with respect to the principal axis is $\alpha \text{ rad}$. The value of $\alpha$ is $\frac{\pi}{n} \text{ rad}$,where $n$ is:

DifficultIIT 2022

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In the displacement method,there are two positions of a lens for which we get a clear image on a screen. If the first position of the lens is at $40 \, cm$ from the object and the second position is at $80 \, cm$ from the object,the focal length of the lens is ......... $cm$.

Medium

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If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

When blue light is used instead of red light in a convex lens,its focal length will ......... .

In the displacement method,there are two positions of a lens for which we get a clear image on a screen. If the first position of the lens is at $40 \, cm$ from the object and the second position is at $80 \, cm$ from the object,the focal length of the lens is ......... $cm$.

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