(D) For a concave lens,the focal length $f = -16 \ cm.$ Since the light rays are converging at point $P$ behind the lens,the object for the lens is a

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(D) For a concave lens,the focal length $f = -16 \ cm.$ Since the light rays are converging at point $P$ behind the lens,the object for the lens is a virtual object. Therefore,the object distance $u = +12 \ cm.$ Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ Substituting the values: $\frac{1}{-16} = \frac{1}{v} - \frac{1}{12}$ Rearranging to solve for $v$: $\frac{1}{v} = \frac{1}{12} - \frac{1}{16}$ Finding a common denominator: $\frac{1}{v} = \frac{4 - 3}{48} = \frac{1}{48}$ Thus,$v = 48 \ cm.$ Therefore,the beam converges at a distance $x = 48 \ cm$ from the lens.

Class 12 Physics Ray Optics and Optical Instruments Refraction by Lenses

Medium

The figure given below shows a beam of light converging at point $P.$ When a concave lens of focal length $16 \ cm$ is introduced in the path of the beam at a place $O$ shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to.....$cm$.

A
$12$
B
$24$
C
$36$
D
$48$

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Class 12

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Ray Optics and Optical Instruments

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Refraction by Lenses

In an experiment to measure the focal length $(f)$ of a convex lens,the least counts of the measuring scales for the position of the object $(u)$ and for the position of the image $(v)$ are $\Delta u$ and $\Delta v$,respectively. The error in the measurement of the focal length of the convex lens will be:

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If a concave lens is placed in the path of converging rays,a real image will be produced if the distance of the pole from the point of convergence of incident rays lies between ($f =$ magnitude of focal length of lens).

Medium

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$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $^a{\mu _g}$ and $^a{\mu _l}$ respectively,then

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For a convex lens,the distance of the object is taken on the $X$-axis and the distance of the image is taken on the $Y$-axis. The nature of the graph so obtained is:

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$A$ converging lens forms an image of an object on a screen. The image is real and twice the size of the object. If the positions of the screen and the object are interchanged,leaving the lens in the original position,the new image size on the screen is

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If a concave lens is placed in the path of converging rays,a real image will be produced if the distance of the pole from the point of convergence of incident rays lies between ($f =$ magnitude of focal length of lens).

$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $^a{\mu _g}$ and $^a{\mu _l}$ respectively,then

For a convex lens,the distance of the object is taken on the $X$-axis and the distance of the image is taken on the $Y$-axis. The nature of the graph so obtained is:

$A$ converging lens forms an image of an object on a screen. The image is real and twice the size of the object. If the positions of the screen and the object are interchanged,leaving the lens in the original position,the new image size on the screen is

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